Dr Pepper, to fix your problems just boot the PS2 up without a disc in the drive, and go into Settings. You need to tell the PS2 that you are using component video (YCrCb/YPrPb) rather than the default setting (which I think is RGB?). Then things should work correctly.
With respect to the image quality discussion, I can honestly say that I have NEVER been able to notice any difference between composite (RCA) and S-Video, so my advice is not to bother with S-Video. However, the jump to component is worth it, as the difference is huge, especially with respect to colour bleeding.
I have a 27" LCD that doesn't support HDTV (using YCrCb through a SCART connector), and GT4 is especially grainy on it during racing (not replays) compared to other PS2 games, including other racing games like Midnight Club 3. However, I do sit less than 2' from the screen (no space to sit further back unfortunately). The problem I guess is that LCDs are much sharper, and so some defects in the graphical filter being used are more apparent as opposed to CRT and projectors, where you get a softer and slightly blurrier picture. This seems to vary by game. For example, the graphics filter in Resident Evil 4 looks great on my LCD, but absolutely shocking on my friend's projector.