It's most likely the eye....here's what you do.
Unscrew the bottom of the ps2...there's 8 screws all together...6 on the bottom platform..and 2 next to it on the overhang. Next....unscrew the top of the disk ejector...they're tiny screws..I think 6 of em...don't lose em! Next, with a q-tip, dab one end in rubbing alcohol and gently wipe it on the eye....next..with the other side of the q-tip, dry off the eye and make sure it's no longer wet at all. Next, re-assemble and the games should run smoothly.