Romans 7:17 KJV
Now then it is no more I that do it, but sin that dwelleth in me.
In the last half of this chapter Paul describes the war between "Saul of Tarsus" and "Apostle Paul." The battle was real and it was going on even in one used of the Lord so much as Paul. The chapter ends with Paul in defeat. The old nature is winning and his hope is not in the flesh but in Jesus Christ.
That is where every believer today ought to find themselves. We cannot win this struggle in the power of the flesh because it is in fact a struggle against the flesh.
But this war (with the flesh) must be maintained - this is no reason for surrender. We do not give in to the flesh because we cannot defeat the flesh but we mortify the deeds of the flesh more and more.
The law is not sin. Obedience to the law of Christ (as opposed to the law of Moses) is the expectation of the Father upon us. May God grant us the strength of the Holy Spirit to mortify the deeds of the flesh.