AND IF CHRIST IS IN YOU THOUGH THE (physical, mortal) BODY IS DEAD BECAUSE OF SIN: ei de Christos en humin to men soma nekron dia hamartian: (Torrey's Topic Union with Christ) (John 6:56; 14:20,23; 15:5; 17:23; 2 Corinthians 13:5; Ephesians 3:17; Colossians 1:27) ((11; 5:12; 2 Corinthians 4:11; 5:1-4; 1 Thessalonians 4:16; Hebrews 9:27; 2 Peter 1:13,14; Revelation 14:13)

And is probably better rendered "but" (1161) as it indicates a contrast to what Paul has said before. Note that he now begins to address the reader as "you", indicating that he is speaking to believers

The subject that Paul is dealing with in this verse is how the “dead” body, in which sin dwells, can also be a vessel of the life of God. His answer is in the next verse. It is the Holy Spirit Who gives life to our mortal bodies.

"If" (1487) (ei) defines a condition of the first class or one that is assumed to be true. If can be understood as since or because. If does not express doubt but indicates that He is in the believer.

Since "Christ is in you" means that Christ Himself is in us. The indwelling of the Holy Spirit is the indwelling of Christ Himself. Compare Paul's statement in Ephesians 3 where he prays that the Father...

would grant you, according to the riches of His glory, to be strengthened with power through His Spirit in the inner man so that Christ may dwell in your hearts through faith; and that you, being rooted and grounded in love (Ephesians 3:16-17)

In Colossians Paul stated the same truth writing that Christ had been made known to the saints...

to whom God willed to make known what is the riches of the glory of this mystery among the Gentiles, which is Christ in you, the hope of glory. (see note Colossians 1:27)

In Galatians Paul reiterated this truth declaring...

"I have been crucified with Christ; and it is no longer I who live, but Christ lives in me; and the life which I now live in the flesh I live by faith in the Son of God, who loved me, and delivered Himself up for me. (Galatians 2:20)

Body (4983) (soma) refers to an organized whole made up of parts and members. Here soma refers to human the body which is the external man, the human frame which contains the seeds of decay and is mortal, doomed to death, in time due to sin.

Dead (3498) (nekros from nékus = a corpse = English - necropsy, necrophobia, etc) refers to that which is literally dead even though that end has not yet been realized. Nevertheless the forces of death are working in our bodies and they will all inevitably die, except those whose bodies are are raptured.

The reference to the body as dead because of sin is clearly a reference to its ultimate destiny by the infliction of the penalty of sin (cf. Ge 3:19; see note Romans 5:12).

Godet writes that...

The term dead here signifies: irrevocably smitten with death. The human body bears within itself from its formation the germ of death; it begins to die the instant it begins to live. (Godet, F L: Commentary on Romans. Kregel. 1998)

Matthew Henry has some interesting comments about the body...

is a frail, mortal, dying body, and it will be dead shortly; it is a house of clay, whose foundation is in the dust. The life purchased and promised does not immortalize the body in its present state. It is dead, that is, it is appointed to die, it is under a sentence of death: as we say one that is condemned is a dead man. In the midst of life we are in death: be our bodies ever so strong, and healthful, and handsome, they are as good as dead (Heb 11:12), and this because of sin. It is sin that kills the body. This effect the first threatening has (Ge 3:19): Dust thou art. Methinks, were there no other argument, love to our bodies should make us hate sin, because it is such an enemy to our bodies. The death even of the bodies of the saints is a remaining token of God’s displeasure against sin. (Henry, M. Matthew Henry's Commentary on the Whole Bible)

Those who have Christ in them now have a brand new vitality. Yes, our mortal, physical bodies are dying because sin killed our bodies, but our spirit is alive because Christ lives in us and the righteousness of God has been imputed to us. "Therefore we do not lose heart, but though our outer man is decaying, yet our inner man is being renewed day by day" (2Cor 4:16), growing stronger because of the life we have in our bodies from the Spirit of God.

William Newell notes that in this verse...

"...we have the answer to our Lord's prayer in John 17:21-22: "I pray . . . that they may all be one; even as Thou, Father, art in Me, and I in Thee, that they also may be in us: ... that they may be one, even as we are one." We have seen in an earlier chapter how we came to be in Christ: that God, having ended our history before Himself as connected with the first Adam, at the cross, created us in Christ, the Last Adam, the Second Man. Thus was the one part of our Lord's intercession answered. We are in Christ. But the other part of the great mystery is here before us in Romans 8.10: Christ is in us. Although, as we know, He is within us by His Spirit, yet it is Christ Himself who is in us." (Romans 8: Expository Notes Verse by Verse).

Sin (the principle) still lives in these "dead" and dying bodies. Spurgeon put it this way...

"There is no doctrine more true to experience than this, that corruption remains even in the hearts of the regenerate, and that when we would do good evil is present with us...We are often like a glass of water which has been standing still for hours and looks very clear and bright. But there is a sediment, and a little stir soon discovers it and clouds the crystal. That sediment is the old nature."

One day soon we will receive our glorified body and then sin's presence and pleasure will be forever totally eradicated. Lord haste the day!

Moule commenting on this verse writes that...

But if Christ is, thus by the Spirit, in you, dwelling by faith in the hearts which the Spirit has, “strengthened” to receive Christ (Ephesians 3:16, 17) — true, the body is dead, because of sin, the primeval sentence still holds its way “there”; the body is deathful still, it is the body of the Fall; but the Spirit is life (see discussion below whether Paul means Spirit of God or man's spirit), He is in that body, your secret of power and peace eternal, because of righteousness, because of the merit of your Lord, in which you are accepted, and which has won for you this wonderful Spirit-life. (Moule, C. G. The Epistle of St Paul to the Romans. Ages)

YET THE SPIRIT IS ALIVE BECAUSE OF RIGHTEOUSNESS: to de pneuma zoe dia dikaiosunen: (John 4:14; 6:54; 11:25,26; 14:19; 1 Corinthians 15:45; 2 Corinthians 5:6-8; Philippians 1:23; Colossians 3:3,4; Hebrews 12:23; Revelation 7:14-17) (5:21; 2 Corinthians 5:21; Philippians 3:9)

Literally this reads "yet the spirit is life".

Matthew Henry writes that...

the spirit, the precious soul, that is life; it is now spiritually alive, nay, it is life. Grace in the soul is its new nature; the life of the saint lies in the soul, while the life of the sinner goes no further than the body. When the body dies, and returns to the dust, the spirit if life; not only living and immortal, but swallowed up of life. Death to the saints is but the freeing of the heaven-born spirit from the clog and load of this body, that it may be fit to partake of eternal life. (Ibid)

Yet (1161) (de) emphasizes the contrast between these preceding statement (body dead because of sin) and this statement (spirit is alive because of righteousness).

Some favor that "the spirit" refers to the person's spirit while others favor a reference to the Holy Spirit (observe this difference of opinion in the translations above, where some capitalize Spirit and some do not). In a sense although I favor the human spirit, there is a sense in which the Holy Spirit is also correct because the human spirit, having been quickened at regeneration, is possessed of the inalienable principle of life, but only by virtue of the power of the Holy Spirit of God. That said here are a few conservative commentators who argue for spirit with a small "s".

Wuest favors a "small s" writing...

The word here refers, not to the Holy Spirit which is not a logical contrast to the human body, but to the human spirit, that part of man which gives him God-consciousness and enables him when that spirit is made alive by the Holy Spirit, to worship God. The believer’s human body is dead in the sense that it has death in it because of sin, Adam’s sin which brought both spiritual and physical death to each member of the race. The believer’s spirit is alive (zoe) in that the Holy Spirit energizes it with divine life which is righteous in its quality. Eternal life is not only unending in its nature, but also ethical and spiritual in its content. (Wuest, K. S. Wuest's Word Studies from the Greek New Testament: Studies in the Vocabulary of the Greek New Testament: Grand Rapids: Eerdmans)

S Lewis Johnson agrees noting that...

The word "spirit" in the clause, "but the spirit is life because of righteousness," is probably a reference to the human spirit and not the Holy Spirit, although that is the interpretation of the translators of the Authorized Version, for they capitalize the word. The contrast with body makes the reference to the human spirit likely, but the human spirit as regenerate. It is given new life in regeneration (cf. John 6:50-51; 11:26). (Romans 8:5-17)

Charles Hodge also agrees writing that...

By spirit here Paul does not mean the Holy Spirit, but the human spirit, since it is contrasted with body in the former clause. The body is dead, but the spirit is alive. It should not therefore be printed with a capital S, as in the KJV. The sense in which the spirit is life is antithetical to that in which the body is dead. As the body is infected with a principle of decay which renders its dissolution inevitable, so the soul in which the Holy Spirit dwells has a principle of life which secures its immortal and blessed existence. (Hodge, Charles: Commentary on Romans. Ages Classic Commentaries)

Alive (2222) (zoe) is literally "life" as opposed to death in previous section. It is the state of one who is possessed of vitality or is animate. Note that this verse reads more literally "the spirit is life".

Godet writes that...

The life of God does not become merely an attribute of the spirit in man through the Holy Spirit; it becomes his nature. (Godet, F L: Commentary on Romans. Kregel. 1998)

Denny writes...

“God-begotten, God-sustained life” (Denney), if Christ is in you.

Paul explains to the Ephesians that God...

even when we were dead in our transgressions, made us alive together with Christ (by grace you have been saved), and raised us up with Him, and seated us with Him in the heavenly places, in Christ Jesus (Ephesians 2:5-6)

Righteousness (1343) (dikaiosune) in Biblical terms describes the righteousness  acceptable to God which means it is in keeping with what God is in His holy character. Because Christ is in us and He is perfect righteousness, we have been declared right with God -- that is, because of the divinely-imparted righteousness by which every believer is justified (see note Romans 3:21-23; 3:24-26). The eternal, spiritual life of God is implanted by the indwelling Holy Spirit and Jesus Christ here and now, even though a believer’s body is mortal.

S Lewis Johnson adds that...

The righteousness is both imputed and imparted, for in the context the apostle has had in mind both justification and sanctification and their indissoluble connection. (Romans 8:5-17)

Leon Morris agrees commenting that...

The believer is credited with “the righteousness of God”; it is this that brings him into the sphere of salvation (justification). But then he is required to live a life that is in conformity with this salvation (sanctification); he cannot be indifferent to the importance of righteousness in his daily living. At this point it may well be that Paul has in mind neither the process that brings salvation, nor the life that follows, but both. (Morris, L. The Epistle to the Romans. W. B. Eerdmans; Inter-Varsity Press)

Many Christians do miss out on living their Christian lives in the constant fullness of the Spirit, because they are not constantly being filled with the Holy Spirit as Paul commanded in (Eph 5:18). They fail to experience  what Jesus spoke about when He described rivers of living water flowing from the believer (Jn 7:37-39).