Ugh... that sucks. Sadly, PS2 games will look like garbage on larger TV's no matter what you do; however better cables can help to an extent. I have mine hooked up to a 42" LCD via component and I get sharper text but the images, save for extra-detailed cutscenes, are still junk. In fact, a buddy of mine watching me play FF XII yesterday told me I needed to ditch the large HD screen and get a crappy 19" so the graphics look better! He's almost right.
I also doubt that digital video cables exist for the PS2. I discovered that a lot of video game resolutions, including the PS2's 480i/p, simply don't convert. I have a receiver that converts all inputs into HDMI, but the manual specifially says most video game resolutions are not convertable; and so I can only assume that implies the limitation on digital cables. Of course, I could totally be wrong but this is based on my own experience trying to run my PS2 to my receiver via component; then from receiver to TV via HDMI.