Does the PS1 work on the same TV in the same socket that gives the PS2 the wrong colours? If so then the PS2 has a duff connector... So any thoughts of using an RGB signal from it are pointless.
Your GFX card has a DVI output not an input. Your monitor MIGHT have a DVI input and a VGA input though - a lot of LCDs have both - not very many CRTs do though... if it does then get a DVI lead for the PC and the PS2 can use the VGA input on the monitor all to itself.