After the restore, the PC would get to the XP splash screen, and in about 2 seconds would reboot. Forever. It did the same in all three versions of safe mode. So I invoked the F8 "do not resuscitate" option, popped in the XP CD again, and started from scratch.
Nuked the partition, re-created it, formatted, installed XP SP1 (I have a separate SP2 CD), this time only restored the files, not the system state. That worked. Sort of. It did not restore the registry, but all I had to do to re-enable the device drivers was right-click on each one and choose "update".
The machine was still in SP1, so I loaded the SP2 CD. I left the apartment with Microsoft Update installing about 80 updates. As I was driving to work I realized I should be able to use System Restore to get back my registry, now that the restore points are back on the hard drive, all 2,687 of them.