I got my PowerBook back today. They had to replace the motherboard. Since it’s still under warrantee, there was no charge for the repair.
I notice that System Profiler no longer reports a serial number. Poking around with IORegistry Explorer shows that the serial number strings aren’t present. I didn’t deauthorize it for iTunes Music Store before I had it repaired, and now iTunes thinks it isn’t authorized. Thankfully I haven’t reached my limit for number of authorized machines, although I probably will with the Mac Mini.