I'm not positive, but the best way to hook up a PS2 to a moniter is with a VGA Box. I know the dreamcast had one, I know the XBox has one, unsure about the PS2 and Gamecube tho. Hooked up my Sony 21" to my old dreamcast with a VGA box, LOOKED AMAZING. I only hope you can find a VGA box for a PS2.
Other options are available, but honestly they won't look nearly as good.