Considering that you are not a believer, and more importantly have no plans to become one, there is likely no answer that you will find acceptable. (Although I appreciate noting your bias) These are articles of faith and are answered on a personal basis as each person reconciles the often troubled world we live in with their perception of God and his purposes.
For the atheist, (FTR I am not one, nor do I want to speak presumptuously for them) this may very well be more evidence that there is no God.
From your example, I do not know what is going on here. The more global question you posed as to why God listens to some prayers (apparently) and not to others can be answered in part in the bible. (Of course, if you don’t believe in the bible this will offer nothing in the way of an acceptable answer)
God expects our prayers to be consistent with his will and purposes. (It is after all, his universe…) Jesus gave us a prayer, commonly called the Lord’s prayer, to serve as a “model.” (Matt 6:9-13) He prefaced it by saying that we shouldn’t say it by rote. (Matt 6:7) It is important however that our prayers be in harmony with his will. (1 John 5:14, 1 John 2:22, Proverbs 28:9) You would not, for example, pray for harm to be done to someone, or to pray to win the Super Lotto. It’s worth noting that the first 3 things noted by Jesus at Matt 6:9- involve God’s name, his kingdom and the advancement of his will. (before going to more basic needs like “our daily bread.”)
It is true that we must make an attempt to be doing God’s will for our prayers to be answered. (1 Pet 3:12, 1 John 3:22, Jas 4:3) We must also remember that not all prayers are answered immediately like a spiritual FedEx. It is important to persevere in prayer. (Matt 26:42, Phil 4:6, 1 Thess 5:17,18) Often we are “self absorbed” and that is often reflected in our prayers. A fundamental part of being a Christian is to become more selfless and develop an attitude of service towards God, and then to our fellow man, before ourselves. (Ps 25:4,5, Luke 11:2)
All of that is pretty much moot to a young girl is who is being molested, or a senior citizen who is starving. So what does (if he exists) God allow suffering to continue, or why do good people often seem to get screwed? It’s worth noting that this world’s misery is not of God’s doing. We inherited sin and death (and of the messy things that come from imperfection like rape and starvation) from our original parents. (Rom 5:12, Rom 6:23) That is not to say (and I’ll italics it lest someone say the little girl in your example “had it coming to her”) that God is unconcerned with our plight and doesn’t offer us some hope for the future. But the fact is that we are all given the gift of “choice” and our original parents “chose” to put themselves, and by extension us, in this bind. Satan has been the primary architect of this rebellion. (Acts 10:38)
Yet God has offered us the chance to live in a world where this misery is gone. (Ps 37:29, Ps 37:10-12) It might seem to us, escpecially when we are suffering, that God is unconcerned, or non-existent. However his will is being worked out and in his time relief for mankind will come. (2 Pet 3:9, John 5:28,29, Rev 21:4,Isa 65:17) He is not slow regarding his promises, although it surely can seem that way sometimes.