By sending his Son, God accomplished what the law could not. But to what does the law refer in this Romans 8:3? Law may refer to the Mosaic Law, keeping to the context of Romans 7:1-12 or as a “principle” as in 7:21 (the “sin principle”).
James Dunn and N. T. Wright argue Paul is consistently contrasting the Mosaic Law (or at least the boundary markers of the Law) in Romans 7 and it makes sense he should continue to contrast the written code (7:6) and the law of the Spirit. Although the Law promised life to those who kept it perfectly, it was powerless to deal with the real problem facing humanity, the problem of sin.
Colin Kruse argues the second view is preferable since it makes Romans 8:1 a continuation of 7:21-25. There is a principle at work in the people who desire to do what is good, but find themselves doing what they know to be wrong. The person who is in Christ is freed from the sin principle (7:25) and is not able to be punished for that sin principle because it has been fulfilled by Christ.
A problem is Paul’s description of the Law as weak (ἀσθενέω, v. 3). The verb refers to something that is weakened, perhaps by illness. This is often the word-group used in the Gospels for those who are healed by Jesus. But Paul uses the word for any kind of weakness or inability, including the “weak brother” in Romans 14 who is unable to eat meat due to their conscience. In chapter 7 the purpose of the Mosaic Law was to define sin so that humanity could be justly punished and know they are in need of a savior. That is not a weakness or inability, but rather the purpose for which the Law was originally designed.
In either case, this law is powerless to set people free from the power of sin which results in a downward spiral into more sin and finally in death.