The original, white Core 2 Duo from 2006? Does it "bong"? If not, the Radeon X1600 is probably shot. A reflow may fix it, may not. If it does "bong", the backlight inverter may be shot keeping the display from lighting. I've had one that had half of the backlight inverter fail so the screen was dim. With a failed inverter, you should be able to see the image on the screen by holding a flashlight very close to it.

Those would be the common display problems, I believe.

If you think that the problem is with the inverter and it is the white, 20" C2D from 2006, send me a PM because I think I have the inverter you need.