does God hear the prayers of nonChristians?

No. Scripture is replete with texts clearly stating that the only way to God the Father is through Jesus Christ. Period. No other way is acceptable. Not only does this include salvation but it also includes coming before the Father in prayer.

Last night I preached on evangelism and how it is imperative for the Christian to have a burden for the lost and share the gospel with unbelieving friends, family, and strangers. Afterward, one individual approached me and asked if God hears the prayers of good moral people who are not Christians. I responded by saying: "no."

John 14:6 6 Jesus said to him, "I am the way, and the truth, and the life; no one comes to the Father but through Me.

1 Timothy 2:5 5 For there is one God, and one mediator also between God and men, the man Christ Jesus,

Ephesians 3:11-12 in Christ Jesus our Lord, 12 in whom we have boldness and confident access through faith in Him.

These verses state that it is only through Jesus that anyone can approach God the Father in prayer. It is only those who are redeemed and forgiven and washed who have access in confidence before the Father in prayer (cf. Eph 3:12). You may ask, "well, how does someone get saved, then, if God only hears the prayers of believers?" Good question. At the moment of conversion, when the Holy Spirit miraculously, instantaneously, and supernaturally regenerates the deadened heart and instills salvation in that lost soul, God hears that sinner's cry of repentance and reconciliation and He eagerly forgives and instantly lavishes every spiritual gift on that person (cf. Eph 1:3). But that's at the moment of conversion. Before that, God is deaf to the prayers of nonChristians—indeed, every religion that rejects Jesus Christ as the only way of salvation is false and their prayers are impotent. Moral people nowadays who pray and ask God to help them through their specific 'financial crisis' fall upon deaf ears of God. Why? Because they have no one to plead them before the Father. Their access before the sovereign throne of God Almighty is forbidden.

The solution? Repent, confess, and believe in Jesus Christ! At the moment of saving faith, all access is granted to the sinner to have boldness in speech and access in confidence before God from that moment on—continuing into eternity!

So then, heed the words of Auctor:

Hebrews 4:15-16 15 For we do not have a high priest who cannot sympathize with our weaknesses, but One who has been tempted in all things as we are, yet without sin. 16 Therefore let us draw near with confidence to the throne of grace, so that we may receive mercy and find grace to help in time of need.