I have a similar problem. When I got my cheap Olevia hdtv I couldn't play PS1 games at all. Basically the games show up on the upper right corner of the screen and it looks screwed up while the PS1 logo stays in the background (and I get sound). I was told that this happens because my tv cannot display the PS1's resolution properly over component.
Can you try out the PS2 with Svideo/composite to see if it works that way? I don't have those cables so I can't try that. If you have them you can give it a go and see if you get the games looking good with S-video or composite.
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