I just resolved this problem with mine today by replacing the display data cable. I had to follow the 17 pages of directions here, then a few more pages from this PDF: http://www.PowerBookmedic.com/xcart1/files/PowerBook_G4_DVI1.pdf
The worst part of this is that you have to disassemble the LCD housing (the lid) and it's glued together with epoxy. Mine didn't turn out TOO bad but it's definitely battle scarred now. It did work, by the way, but it took me over 7 hours to do the repair and I'm no newbie.