shneady has some good advice. Check the Apple support pages for how to reset the PRAM if your battery is not removable.
Do you have AppleCare (or still in the first year)? If so, give them a call... you paid for it, may as well use it.
There is an extended hardware test on the installation CD. AppleCare can talk you though it, or if you don't have AC, search the Apple Support pages. There is a wealth of information there, and most questions like this can be answered there. I would tell you how to do it, if I knew, but I don't.
Good Luck.