Why not get a component cable, use the built in digital out and the buy a component to VGA adapter? I'm not sure what to do about the sound unless you have to use the A/V cable and just use the red and white at the same time.
If your GC is newer than May 2004 you are out of luck. http://www.nintendo.com/consumer/systems/nintendogamecube/component_faq.jsp





