Bad actions by bad people don't prove God exist or does not exist.
No, but it does prove god isn't intervening, and since answering prayers is intervention, god clearly isn't answering any prayers whatsoever, period!
Therefore, a totally non-intervening God is irrelevant. Such a being may as well not exist at all. So stop wasting your time praying to this aloof, non-intervening, hidden god or defending it or vainly trying to prove if it event exists or not. Clearly, this god is not listening.
The answers lie within, in our own conscience and mind and hearts. We've got to help ourselves and stop suffering and evil as best as we can.
This is basically the buddhist and humanist position.