I'm still on the original model of PS2, it's buggered up 3 times now and I've fixed it very easily.
Basically you need to turn it upside down, take off the rubber feet, unscrew everything and open it up. Take off the cover over the disc tray and then take a can of compressed air to the thing, especially the laser. The problem with the old PS2s is that thanks to the way it's ventilation worked, over time dust would build up on the laser.
And if that doesn't fix it you had to middle with the little gear that changed the laser height.
[Edit: Also buck, the ps2 came out in 2000.]