I'm agnostic, I neither believe nor disbelieve the existance of a god. Under your definition, I am also an atheist, as I lack a belief in God. And as I discussed with Snoopster, Skepticism in the theological sense, is doubt as to the existance of God or gods, basicly an agnostic who leans toward atheism.
Disbelieving something and not believing it are the same thing; the former is simply the language's way of positively phrasing the latter.
No, what I was saying is that to someone with true faith, no evidence you could give would be enough to convince them God doesn't exist. And to a committed Atheist, no proof would be enough to convince them of the existance of God. They are religous extremes. They are extremely rare in real life, as most people have some doubts in their belief (or lack there of).
As for the question of belief, there is no way to prove or disprove the existance of God. Take the question that my religion teacher liked. What caused the Big Bang ? And if you know, what caused that ? Or caused the thing before that ? Keep going back and sooner or later, you reach a point where no-one knows. A person who believes in God would believe God started it. An atheist would believe it was something else. As there is no proof one way or the other, the person would have to believe their view. The atheist would BELIEVE there was no god. To accept without evidence.
Of course there isn't, but that's just as true of leprechauns, Santa, and the tooth fairy. That's no reason to believe in any of the four.
As for your point about the Big Bang, it's just wrong. Causality is a result of spacetime, and spacetime is a result of the Big Bang. Causes did not exist until 'after' the Big Bang. Nothing caused the Big Bang because causes didn't exist.
The point about beliefs is, there is absolutely no evidence supporting the existence of a God. Therefore, it is not rational to believe in one. Atheism is the rational position, and it is also the natural position--people are born without a belief in God.
Yet each man kills the thing he loves--
By each let this be heard...
The coward does it with a kiss,
The brave man with a sword!