I have this same problem. Nothing works. I thought it was because I installed too many fonts (8000) because once i removed them it worked fine. Now it doesn't. I have tried EVERYTHING. It is not the trackpad, the batteries, etc. It has a brand new hard drive and 6 gigs of ram. That's not the problem either. I wonder if Apple runs diagnostics for free? (at the genius bar)
btw. My buddy is bringing my snow leopard disc over now. Going to see if I can run disk utility from the disc or I may have to just install and do everything fresh. I really don't want to lose everything though and if there is a problem I sure it is bigger than snow leopard. So how exactly can I check if the logic board is going out or if something is screwing up my system? Like i said, I have done everything suggested and I still only get my desktop.
When I try to click anything (including finder and the apple in the menu bar) my screen just goes away, comes back and blinks every time I try to click. Safe Mode doesn't work either, same thing.