For the record, I consider myself to be a skeptical agnostic.
Consider a Universe in which God does not exist.
Those who wish to disprove the existence of God claim that we live in such a universe.
Now consider a Universe in which God exists, but He* chooses not to intervene in any way perceptible to man.
The two universes are, by definition, indistinguishable, and thus, there is no way to prove that we live in the former.
Thus, there is no way to prove the non-existence of God.
*The capitalized singular masculine pronoun 'He', generally associated with the Christian God, is used for convenience. This argument applies to any omnipotent, omnisicent being.