Starting at verse 1 I hit the word "Therefore." Therefore what? Therefore logically follows something else, saying, "in consequence of that." In consequence of what? A quick glance back at the second half of 7:25 provides reasoning for Paul to use the word "therefore."
"So then, I myself in my mind am a slave to God's law, but in the sinful nature a slave to the law of sin."
Therefore! It may seem overwhelming to think that you want to do what is right mentally but are bound by your sinful nature. Paul knows how this feels (Romans 7:14-20). For that reason, he slams the word therefore in there. You may be a slave to sin, but don't worry, the Spirit of Life frees us from that sin. The Spirit that works through the power of Christ.
"1Therefore, there is now no condemnation for those who are in Christ Jesus, 2because through Christ Jesus the law of the Spirit of life set me free from the law of sin and death."
God set up the law for his people to follow. His people sinned and this sin weakened the law. God saw the need to satisfy this law so we could draw near to him.
Hebrews 7:18-19: "18The former regulation is set aside because it was weak and useless 19(for the law made nothing perfect), and a better hope is introduced, by which we draw near to God."
So, the Holy Spirit has cleansed us of our sinful nature through the incredible power of Jesus. Jesus' power came from conquering death in the form of sinful man while not sinning. A result of these two working together is seen in verse 4: "in order that the righteous requirements of the law might be fully met in us, who do not live according to the sinful nature but according to the Spirit."
How awesome is this series of events? Christ fulfills the law so we can draw near to God and be counted righteous because of him. Once we accept that Christ did this for us, the Holy Spirit of God comes into our life and cleanses us, frees us, to accept that righteousness that Christ prepared. How unbelievable... The God of the universe, of quasars and neurons, of bee hummingbirds and blue whales, set all of this in motion because he wanted you. He wanted to be close to you. He loves you and wants a personal relationship with you. How incredible.