I've never heard of something like this occuring before. Don't take your disc in if it doesn't have any scratches, cuz I doubt it'll be that. It's most likely the PS2. The problem with mine was there was too much dust in it. If you used the can of air then it's probably something else. My brother smokes in his room and the smoke built up on the inside caking it with resin and destroying any chance of playing a game glitch free. Do you smoke?

Other than that I'd say that it could be something got knocked loose (but don't quote me on that cuz I really wouldn't have a clue). Maybe you should try testing more than just two games on it and see if it is the PS2 or just the disc.