An overwhelming problem with most people that don't believe the Bible when they read it, is that they do not treat it with the same objectivity that they treat other works. Instead they are veiled by their own preconceptions of what is possible and what is not. The first of which is that they place limits on what the scripture teaches is a limitless God. Enacting those limits quickly places the entire text into question. In essence they create God with the same limitations they place on themselves, thus creating God in their own image. Modern "science", betrays itself in that it makes an assumption (i.e. that there is no God) before it looks at the experiment (mankind, nature, the universe), then makes a judgement based on that predisposition. If science were truly science, it would discount nothing, even the existence of a limitless God.
The primary problem is not that we (collectively) cannont believe in the existence of God based on the facts, but that we (collectively) choose not to despite the facts. It is a problem of our will, not a problem of our intellect.
Take the Bible at face value, with no prejudices, and you will find that it is emminently believable.