Answer: We would not have a Bible if God were unwilling to communicate with sinners! Scripture was inspired and written specifically so that all humans would have the means to come to repentance and change their ways. The Bible is full of examples where God was not only willing to hear sinners but also, in some cases, to initiate contact and talk with them!
God initiated a discussion with both Adam and Eve after they became sinners by eating of the tree of good and evil (Genesis 3:8 - 19). God also initiated a conversation with Cain after his offering was rejected (Genesis 4:6 - 7) and after he murdered, in cold blood, his younger brother Abel (verses 9 to 15).
The Lord was also willing to speak directly to Eliphaz, one of Job's three friends, in order to reprimand him for speaking lies during Job's trials (Job 42:7 - 8). King Hezekiah of Israel prayed that God would heal him of his deadly illness. His petition, given in humility and tears, was heard and he was healed (2Kings 20:1 - 6).
Jesus, as God in the flesh, spent his entire ministry preaching the gospel and calling sinners to repentance (Luke 5:32). He interacted, on a regular basis, with those considered the most disobedient (e.g. tax collectors and harlots, see Matthew 9:10 - 11, 11:19, 21:32, Mark 2:16, Luke 5:30, etc.).
What few people realize is that Jesus, apart from John the Baptist, never spoke to a converted human (someone who had the spirit of God in them) during his entire ministry. This includes both his mother and the disciples, who had his spirit with them but not yet in them!
The truth is, we are all sinners who have fallen far short of his glory (Romans 3:23). Our heavenly Father is more than willing to look upon and respond to those willing to humble themselves before him (Isaiah 66:2). The cries of the poor do reach his ears (Job 34:28).
God has stated, however, that he will not respond to those who are indulging in evil and refuse to repent (Proverbs 1:24 - 28, 28:9, Daniel 9:13 - 14, 1Peter 3:12). In the Old Testament, He warned ancient Israel of the consequences of rejecting him as their King (1Samuel 8:11 - 17). God then stated, because of their refusal to repent, that when they cry out to him for relief from the king they demanded that he would not answer them (1Samuel 8:18).
God does love sinners and hears their prayers and then decides, based on his wisdom, how he will answer them. After all, since the time of Adam, all the prayers that have been directed toward him have come from imperfect humans.