[Coda]

My first guess would be pointing at an issue with your power supply. Fortunately power supplies aren't terribly expensive and are generally fairly easy to replace -- the hardest part is usually unplugging it all because the connectors can sometimes be really snug; actually installing the new one is really easy unless you have a really small computer with funky cable routing.

My second guess would be related to overheating. This is especially likely if these problems don't start up when you first turn the computer on but instead get progressively worse the more you use it. Make sure all the fans are clear and spinning (the air coming out of them should be kinda warm and moving briskly).

Third guess is bad RAM, but this is actually fairly rare compared to the other two problems.

Edit: Actually, if you had a power surge, that makes guesses 1 and 3 more likely, and guess 2 less likely. Your description doesn't sound like the video card itself is damaged, although it's certainly possible.