Think of it, only Christians have a dichotomy, a dual-nature consisting of the old-man and the new-man. These aren't actually persons but parts of a person; they are natures of a person. The old nature we were born with and the new nature we were born-again with.
When Paul said "But now, [it is] no longer I who do it, but sin that dwells in me", I believe the "I" he is referring to is that part of him which is the new nature, which is "divine" (2Pe 1:4), "God's seed which remains in him" (1 Jn 3:9), the one born again. Paul's "no longer I" is that part "which cannot sin", this new nature which now makes up the majority of those "born again". The "born again" refers to us not the new nature. The new nature isn't a person, who can be born again, nor does it require regeneration because it's divine. This is why we aren't ruled by sin (Rom 6:12). We are no longer contaminated by its presence (Ro 7:17, 18, 20, 21), only affected not infected because the Spirit (most precious) by application of Christ's cross keeps sin, which is the old nature, in check , "so that you do not do the things that you wish" (Gal 5:17). This doesn't mean that we will not do wrong. His entire plan includes us being a part of evil so that we might learn the good (Gen 1:26, 3:22). What it does mean is that our wrongs are not willful (Num 15:28, 30; Heb 10:26) and without remorse. Through this "God works in you both to will and to do of His good pleasure" (Phil 2:13).
It has been well said that "His blood procures our pardon from sin and His cross procures power over sin." This is why we (whether we realize it or not) "take up the cross daily"(Luk 9:23). We take it up and the Spirit applies it continually to the old nature. This is where our original nature remains crucified (Rom 6:6). We "are crucified with Christ" (Gal 2:20) but are not still on the cross but the old-man is. "Knowing this, that our old man is crucified with Him, that the body of sin might be destroyed, that henceforth we should not serve sin" (Rom 6:6).
The prime objective is to always remember that the cross of Christ, in the life of those born-again, is the impetus against sin. Not our will power or struggles but what He has done vicariously for us and continues to do by us. Not we by Him but Him by us--big difference. He's using us, not we're using Him! This is also learned by realizing that since it's all vicarious, everything we have of Him in holiness, righteousness and justification are Christ s virtues and are imputed to us, not imparted (Jam 2:23).To impart would require becoming divine, which as we know, will always be reserved for God. We cannot become divine but can only vicariously have a part in it by being "partakers of the divine nature" (2Pe 1:4).
God causes us (Phil 2:13) to do everything by faith in Christ's work, nor ours. This allows us to always cast everything on Him (1Pe 5:7) by believing and reckoning that He causes "all things to work together for good to them that love God, to them who are the called according to His purpose" (Rom 8:28). We can rest in this working of His because He does this regardless of our performance--right or wrong (His teaching tools). His workings are already foreknown and preset due to the vicarious works of Christ for us and not because we please or displease (in our learning) Him. He has already taken all of this into account, before the foundations of creation (Rom 8:29, 30)!