First, let me say that I don't like the phrase 'moral law' very much since it seems to imply that the civil and ceremonial aspects of the law were amoral or even immoral. I don't believe that to be the case at all; however, the term 'moral law' is a common expression and I can't think of another better one to describe those aspects of the law that were meant to govern life beyond the cultus and beyond the civil legal system. In essence, the Ten Commandments serves as a summary of the moral law.
Let me make a short case for the passing away of the civil and ceremonial, as well as the enduring nature of the moral (Even New Covenant theologians who argue for the unity of the law argue to show that thw whole of the law has passed, not that the whole of the law is still in effect). I know of no one who would assert that the ceremonial law continues to be in effect today. Jesus himself declares food laws to be no longer binding, and seems to do the same for the ritual washings (Mk 7). Hebrews seems to make it abundantly clear that the sacrifices and priesthood have passes away as the shadows have given way to the reality.
Moreover, the civil law was given as Israel was being constituted as a nation. God's people were, essentially, of one ethnicity and were being formed into a nation. When, however, you get to the New Testament, what as hinted at in the Old comes to pass - the doors are opened wide and people from every nation enter the church. The church, including Jew and Gentile is a multi-ethnic, global reality. As such, the laws that governed the Jewish nation no longer govern the church. This can be seen, for instance, in how Paul commands the church to deal with the sexually immoral person. In the Old Testament, such an offender of the moral law would be punished severely by the civil authorities. Indeed the death penalty was usually required. However, Paul does not command the church to execute such an offender, but to put them outside the church, cutting them off from the people of God.
So hopefully that begins to explain how the moral law (remember, I'm still not comfortable with that label, but for ease sake I'll continue to use it) differs from the civil and ceremonial and why I believe the ceremonial and the civil have passed away. Obviously more can and maybe should be said, including further examples to prove the point, but I want to move on and make a case for the continued binding relevancy of the moral law on believers today in my next post and then get back to contemplating the benefits of the moral law for believers.