The verdict:
The “Genius” at the Apple Store in Novi, Mich. said the problem was with the “logic board” (motherboard). The iBook is being shipped to an Apple Care Center in Memphis, and will be repaired there.
Thanks again so much for your input, suggestions and help.
This is the very same problem my son had with his g4 ibook last month. While I was using his laptop cruising Free Republic it just stopped. It turned itself off and nothing we could do ourselves or by troubleshooting with Apple by phone would turn it back on. The suspicion was a bad power cord but it was the logic board. We were told that it would be at least a week until a new logic board could be located as this was an issue with the ibook. When a logic board was finally found and installed the hard drive crashed. So a hard drive was ordered and installed. All is well now, and it was all covered by the AppleCare warranty except the information on his hard drive. It cost $55 to have the info retrieved and transferred to the new hard drive. Lesson learned to back up iTunes!