I took my Powerbook into an Apple Store. The "genius" told me that it would be $1400 to get it repaired (he called it a tier 4 repair). This motivated me to get inside the computer myself. I reset the little connectors that connect the display to the motherboard, and the problem has disappeared! I've been working on the machine for several hours. My fingers are crossed. I thought of this trick because I used to work on Apple II computers years and years ago. I'd say 90% of the problems we had with those machines were fixed by resetting memory chips, connectors, and such.