You didn't say what you have, but if it's brand new it's probably a hardware problem--if something goes wrong with any electronics, it's almost always in the first month, give or take.
If it's an old computer (and out of warranty), the Genius bar might be able to give you some suggestions, but it's unlikely to be a software fix. If you're lucky, it's just the hard drive dying (which is possible based on those symptoms), since those are very easy to replace.
I wouldn't really blame Apple too much--you get a bum unit sometimes, that's just the way it goes. Particularly if it's a drive problem, those that have trouble usually run perfectly at first but fail pretty quickly, and Apple has no way of testing for or addressing this other than replacing it under warranty. Same is true for any computer manufacturer.
