Definition of the word "god"
To prove the non-existence of god we first need to define the word "god". When christians talk about god they mean an almighty being. This, I think, is the only god that holds, since it is the only god that can be logically justified.
I think it makes most sense if god is female, because only women can give life. Something that even people in the Stone Age understood. Later when wars affected the cultural evolution, and men took control of society, god became male, but the female god still lives on in the expression "Mother earth". It should also be pointed out that an omnipotent god must be either androgyne or sexless. However, in most religions god is male so I will refer to god as 'he', 'him' etc.
Some people (Einstein for instance) believe in a god who is not a personal god, but a Spinozan kind of god. I claim that this god is not a god! To say that god is universe - by getting knowledge of the universe we get knowledge of god - is to redefine the meaning of the word god. This has nothing to do with the word god as it was defined by the "primitive" cultures which preceded our present civilization. He can be excluded with Occam's razor, and most important: Such a god does not hear prayers.
If god is not omnipotent there is nothing that prevents him from being a product of the universe. If that is the case, what makes god divine? Then god would only be an alien, a being of matter; probably containing flesh, blood and DNA like all life we know of. Everything god is able to do would be things that human beings also will be able to do, all his knowledge would be knowledge we will also achieve. In fact humans would be gods, which should lead to some strange kind of humanism!
Many people justify their faith with god as an explanation. What is the meaning of life? Where does time and space come from? Who created the physical constants? et cetera. Because we lack knowledge of these things - and maybe never will, since they are questions like "what is the color of a second?" or "how does sound taste?" - god is there as an explanation.
Let's say that god is the meaning of life, what then is the meaning of god? If god has a nature, who created that nature? If god created time and space, how can god exist without it? Since creation is an event in time, how could god create time? and who created god? To answer these questions god must be almighty, or else you can't explain them. In fact you can if you say god stands above time and space and so on (which he indeed does if he is almighty), but to be able to prevent god from being tied to future phenomena, you must give him the quality of omnipotence so he can stand above everything.