Hmmm, not too sure about this one, mate.
Are you trying a US or JAP game? If so, your \'problem\' TV might not support 60Hz which is required for these games, hence the jumpy picture.
OR
This may sound daft, but when you trun on your PS2, try flicking through your all your AV channels using your remote control - if I do this, one channel has my PS2 screen slowly moving.
OR
Maybe it\'s just the composite lead your trying. Have you got a mate with a Playstation SCART lead? If so, get a loan of his lead and try using that.
Hope you get it sorted out.