RCA L32WD22 diagonal hd lcd

I had a simliar problem with my xBox, and I own the same TV.  There is a special converter box for the xBox that I recently purchased from a friend of mine.  It converts the signal from the xBox to 720p.  You hook one end to the A/V OUT on the xBox, and you run component RGB and RCA cables for video and sound to your TV.  It now works GREAT!  Perhaps if you searched online, you could find a similar apparatus for the PS2.  Good luck, man!