Does God hear the prayers of sinners?

Many people go to John 9:31 to support the claim that God doesn’t hear sinners (however if you look at who is talking, it is not Jesus, it is a man).  God hears the prayers of sinners every day, because even though a person becomes saved, they are still considered a sinner (1 John 1:8-10).  While sin cannot enter the presence of God (Isaiah 6:5), but He does hear the prayer of the repentant and has done so many times throughout the Bible.  We are told to confess with our mouth the Lord Jesus and believe that He was raised from the dead to be saved (Romans 10:9), we have to pray to God as sinners in order to be saved.  If God did not hear the prayers of sinners, then we all would be in trouble!