Just for the sake of clarity, when you say the screen went 'fuzzy', did you mean blurred (like a steamed-up window), or random pixels lit when they shouldn't be or off when they should be on? I suspect it's the latter, and that it is just a display problem (albeit one that you probably won't want to try and fix yourself).

Oh, and one last thing to waste a little bit more of your time, have you tried a different battery? Yeah, I know, clutching at straws :)