I have an older PS2 - it was a "Network" edition (so, not a "first wave" PS2), and it has played every game I put in it... until I bought Taito Legends. The system simply will not read the disc at all ...
Maybe the dvd drive died? If your warranty is still in place sony will fix it. But be prepared for about a bunch of people saying how crappy the PS2 is and made and stuff btw! Sorry I can't be of more ...