What other output connections does PS3 have?
It *could* be done by using a Component-to-VGA cable but I don't have any experience in using such cable so I can't say fore sure if it'll work. But the basics is that you want to go VGA to Component, with both being analog. DVI and HDMI for digital. If there is more conversion going on, the PQ/TQ can be affected.
My recommendation is to save up and get a descent 27~ 37" LCD flat panel. 720P or 1080P panels should do just fine. And if the PS3 has HDMI output, use that, and connect to the LCD panel.
I own two high-end 50" plasma panels, setup as dual monitors for viewing HD videos and PC games. I'm using SVGA for the plasma 1 and DVI-D for the plasma 2. PQ knock my socks off..