No, of course you cannot prove that god does not exist - and whenever you muster up good arguments, theists are able to counter with numerous subtle tweakings of the postulated nature of the deity - as with the problem of evil, for instance.
I do, however, recall once being, briefly, convinced by the ontological argument for the existence of god - and an exciting moment it was! Bertrand Russell had the same experience once, too - but I believe, apart from legs, arms and suchlike, that that is my only similarity to the Great Man. Oh lord, I am digressing once again...
Anyway, it is damned difficult to prove negatives anyway - which is why science tends to proceed by framing positive hypotheses to attempt to disprove - (insofar as it really proceeds in an orderly manner at all, as readers of books like "The Double Helix" will have cause to ponder.)
I can't prove that s/he/it does not exist - I can only base my position on what seems the most reasonable belief at the time - if we suddenly find phalanxes of angels hiding behind Mars, or there is a second coming with attendant stunning miracles - or something - I shall rapidly revise my agnostic position.
(Here is a brief and extraordinarily unsatisfying reference to said ontological argument, if anyone wants to look - I shall search for a better explanation - if anyone wants me to:
http://www.infoplease.lycos.com/ipd/A0567143.html)