My fat PS2s lens got worse and worse after about a year of purchase, but it still kept reading games for 1 more year. After that it started to have problems reading games, specially new ones like Tekken 5 and such.
The funny thing: if the disc got loaded, and the game started, there was no problem at all while playing, but the problem was getting the darn thing to get to that point.
So i consider it "broken" but i actually still play with games, backed up on the hdd, thats connected to the system, and i also have a slim PS2 i got around the time the fat PS2s lens broke down, now that still works perfectly!