Now we know that whatever the law says it speaks to those who are under the law, so that every mouth may be stopped, and the whole world may be held accountable to God. For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin...Do we then overthrow the law by this faith? By no means! On the contrary, we uphold the law.
Romans 3:19-20, 31
God's law stops every mouth from boasting before God. It holds the whole world accountable for sin. This is a role that it plays even in New Testament times and that it must continue to play today. God's Old Testament law is not null and void. Jesus Himself said,
“Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. For truly, I say to you, until heaven and earth pass away, not an iota, not a dot, will pass from the Law until all is accomplished. Therefore whoever relaxes one of the least of these commandments and teaches others to do the same will be called least in the kingdom of heaven, but whoever does them and teaches them will be called great in the kingdom of heaven." Matthew 5:17-19
It's true that Jesus fulfilled all the law. Parts of the law He rendered inactive or inoperative (see original Greek for Ephesians 2:15) in that their primary function was to separate God's people from the Gentiles as holy and set apart for Him. Other parts of the law had served to point forward to Jesus and His sacrifice and were therefore no longer to be practiced. This is why we don't offer blood sacrifices. Jesus is the only sacrifice we could ever need. Still other parts of the law were civil in nature and were intended to govern Israelite society during the time when God's presence was physically manifested in their midst. These laws required very high levels of holiness and strong punishments for sin (including capital punishment) to avoid God's wrath from breaking out against the entire people because of sin in the camp. BUT the laws that were moral in nature do still apply to us today. Many of these moral laws are quoted or re-emphasized in the New Testament and serve the function highlighted in this passage. They reveal our sin.
Of course, we don't like having our sins pointed out. We hate regret, and we avoid true repentance. That is why we don't often praise God's law like the psalmists did (see Psalm 119 which is an acrostic poem praising God's law). No, we vilify and attack God's law, even in our churches, because we don't understand it or how it works today.
Don't ignore the law or write it off. Let it silence you. Let it make you aware of your sin. Submit to its correction and allow it to shut your mouth before God. Let it serve as a reminder that no one may boast before Him, that no one may think he may be justified by keeping the law. Don't nullify the law; uphold it and its condemnation of your actions! Then repent and draw near to God.
If you want to start fresh in how you relate to God's law, here's a good place to start. Read the Ten Commandments and let them silence you before God (Exodus 20:1-20).