What does St. Paul mean by 'law' in Romans 7?

It is like the difference between law and grace. Law is a written code, with no personality, that demands from intelligent beings that they do certain things: rule one, you must do such and such; rule two, if you do not, you will undergo such and such. Grace knows what the law requires and knows the law will punish no questions asked, but grace also knows that we falter, because of the way we are made. God made us in his image to pay attention to the law, but we are still weak compared to him, who is perfect, so there are times when the image-of-God side of us wants to obey the law and the other side says it is too hard. That is what Romans 7 is all about: I want to do what the law says, but I find within me another law that says I cannot, or that it is difficult. Because God is a personality, a person with feelings, judgment, love, compassion, and pity, he can give mercy to someone who is weak, saying, I am willing to forgive you as long as you are sincere, and so a personal relationship grows. The law can never do that; it is just a statement that says do this or else, with no capability to forgive or show mercy. That is the polarity between law and grace that Paul is describing.