If you're sure your AV cable is OK you may have an issue with the GPU (graphics chip). This isn't usually repairable. Check this thread for descriptions of error codes and possible solutions:
http://forums.xbox-scene.com/index.php?showtopic=484726
We fix PSP's in the store. If you have a "rainbow" LCD (cracked on the inside) you'll need a new LCD screen which runs between $40 and $50. We charge a flat $35 on top of that for the work. I don't normally do mail-in repairs but I'd be willing to do so for a forum member, PM me if you're out of other options.