My PS2 Has Stopped Playing PS2 Games, Only Plays PS1 Games. Is There Some Way To Fix It?

When I try to play a PS2 game, it either tells me it can't read the disc, or it will start to load the game and then goes back to the PS2 menu. All of my PS1 games load fine, however. I have an 80g PS3 but the instruction manual says that it wont play PS2 games, and I can't afford a new PS2. I love many of my PS2 games and want to still be able to play them.