“Why should I pray when God does not hear the prayers of non-believers?"
My answer to that question is that it's based on a false premise. I do not agree that God does not hear the prayers of unbelievers. During the 3-year ministry of Jesus, we see him constantly hearing the cries and meeting the needs of people who did not yet have a saving relationship with him (a few examples: Mark 2:1-12; Mark 5:1-20; Mark 5:25-34; etc.). There are also Bible verses that encourage people to call out to God for salvation - see Psalm 34:6 and Isaiah 55:6-7, for instance. Also, if God does not hear the prayers of the unsaved, then it would be impossible for us ever to lead a non-Christian in a prayer for salvation! To say that an unbeliever cannot expect God to hear his prayers is basically to shut the door of heaven to that person.
Rather than teaching that God does not hear the prayers of an unbeliever, the Bible actually indicates that it is a BELIEVER'S prayers that God will not hear, if that believer is engaging in unrepentant sin (see 1 Peter 3:7, Proverbs 28:9).