In my study of God's Word, I've come to the conclusion that God does not respond to the prayers of an "alien sinner" when asking for God's blessings on himself. However, what are your thoughts on whether God responds to an "alien sinners" prayers when praying for someone else? For example, praying for someone who's extremely ill, especially if the other person is a child of God?
Isaiah explains clearly that when a person sins and remains in that sin, his sins separate him from God. "Behold, the LORD'S hand is not shortened, that it cannot save; nor His ear heavy, that it cannot hear. But your iniquities have separated you from your God; and your sins have hidden His face from you, so that He will not hear" (Isaiah 59:1-2). Thus the problem isn't a restriction on God's ability but on man's refusal to conform to God's will. This is because God finds the prayers of the lawless disgusting. "One who turns away his ear from hearing the law, even his prayer is an abomination" (Proverbs 28:9).
The blind man whom Jesus healed, summed it up well, "Now we know that God does not hear sinners; but if anyone is a worshiper of God and does His will, He hears him" (John 9:31).
Nor will God listen to the prayers of a person contemplating sin. "If I regard iniquity in my heart, the Lord will not hear" (Psalm 66:18). James warns of much the same, "You ask and do not receive, because you ask amiss, that you may spend it on your pleasures" (James 4:3). I've had many people ask if they should pray whether their girlfriend or boyfriend is the one they should marry. Meanwhile, I learn that they are sleeping with said girlfriend or boyfriend. Why would anyone expect God to give approval to a sexually immoral relationship? Yet such questions do not seem to enter these people's minds.
Yet, I don't tell people who have not made their lives right with God that they cannot pray. I tell them it is foolish to pray for approval of their sins or to think that prayer alone is going atone for their sins. They have to leave their sins and mold their lives to God's will. If they haven't become a child of God as God specified, they need to do so. If they are a child of God and have strayed, they need to straighten up. But even in the process, if they pray, at least their mind is focused on God. See the example of Saul. "So the Lord said to him, "Arise and go to the street called Straight, and inquire at the house of Judas for one called Saul of Tarsus, for behold, he is praying" (Acts 9:11).
If a person who is in sin is praying for good to happen, they might not gain an audience with God, but at least they are focusing their thoughts in the right direction.