In chapter 7, Paul argues that death removes certain obligations and opens new opportunities. Because we so identify with our King, who has in fact even died in our place, then we too have died and risen to a new life. This new life is the move in salvation history from a relationship with God governed by the Mosaic Law to a relationship governed solely by King Jesus and the Holy Spirit which guide us.
The Mosaic Law was, in itself, perfect, just and good but, unlike our covenant relationship through Christ, it demanded total obedience without imputing the power to obey it. Thus, the result was knowledge of sin without the power to escape it.
Paul then anticipates the objection that the Law is to blame and is therefore evil. He retorts that it was not the law but sin (or evil) within us that is to blame. The Law then was good in that it specifically pointed out sin but we are weak because we do not have the power to do anything about it, in fact, we take perverse delight in flaunting the specific dictates of the law. I confess that before I became a Christian I darn near used Leviticus as a check list of laws to break every weekend!
In direct contradiction of the proponents of the New Perspective, Paul even uses himself as an example in vv. 14-25 of what his life was like before his redemption in Jesus. Now, he not only knows the ways of God, but has been set free because Jesus perfectly obeyed, took the punishment for his lack of obedience and then even imputes his perfect obedient record to Paul so that he is able to stand in the presence of God whose holiness will not tolerate imperfection. Moreover, the Holy Spirit grants him (and us) power to do good deeds that glorify God and expand His son's Kingdom.