This is an interesting debate.
You cannot prove or disprove the existence of God. There are various reason for it:
1. Nobody actually came to an agreeable definition of the term "God".
2. The definitions of the term "God" that do exist, define him in such a way that you cannot prove or disprove his existence. For example, "God is an almighty entity" statement cannot be tested in scientific ways.
The problem is that a lot of people try to apply scientific logic to religious questions. It simply doesn't work this way. The starting points of science and religion are very different, and each has a very different set of axioms.
Science cannot prove God doesn't exist. As far as science considered, God may exist or may not exist - it won't change a thing, because science is about exploring the world we are living it, and as long as there is a set of rules by which the world works, science will remain useful.
Religion and science are not opposing views of the reality. Religion speaks about how people should behave to please God, and it tells us an interesting story regarding the history of humanity.
Religious people are adepts and settling down discrepancies. For example, a religious paleontologist (yes, there might be some religious paleontologists) will tell you that carbon testing sets the age of this fossil to 4 million years ago. When you ask him how can it be, since according to the Bible the world is only 5700 years old, he will tell you that 5700 years ago the fossil was created 4 million years old. The fossil wasn't NEW when it was created, but it was already OLD. You cannot argue with it. It is a viable option if the assumption that there is an almighty entity that can do whatever it pleases, exists.
I used to teach Astronomy for kids a few years ago, and I had a group of religious 11 year old kids. I asked them why does the Moon rotates around Earth and doesn't just fly away into space, wanting to tell them that gravity works even in space. An 11 years old girl shouted out in defiance: "because God wants it to!". You cannot argue with it. This actually might be the reason. God, if he exists, can turn gravity on and off as he pleases.
A while ago, during my B.Sc, I took a course in the philosophy of science. One of the most important things that I learned there is that all forms of science that base themselves on experiments, are not "foolproof". When we say that "gravity always works according to F=const*m1*m2/r^2", we actually mean "so far we haven't seen a single case when gravity didn't work according to the formula". You cannot "prove" gravity, since gravity is a natural phenomena that we study, and we don't prove or disprove it.
The most basic difference between science and religion is that science is about understanding how the world works, while religion is about how people should live to please God. (and allow me a snide remark - way too often if you please your religious leader, God will also be pleased).