Most likely with these macs its bad capacitors. When you remove the back you will see a lot of swollen caps. they sell the repair kit on ebay if you dont mind changing each and every bad cap.
I have noticed macs are very picky about the kind of ram they accept. Try putting the old ram back and see if it works. Jumping the power padsnot working does not necessarily mean a bad logic board.
Have you tried adjusting the brightness on the screen. If still same issue its possible a blown backlight fuse. I would try another LCD to make sure its not the screen