Clay, I did all three things and now it appears to work. Thanks for reminding me about those basic fixes; I have had so few problems with OS 9 and my iBook that I just don't do the maintenance thing like I once did.
I also zapped and rebuilt on the iBook, and now both Macs exhibit the same behavior: Airport is no longer turned on automatically when the Macs boot. The control strip module says it is on, but I have to turn it off, then on again. I have had this problem in the past but I had not associated it with zapping the PRAM or a desktop rebuild. Eventually Airport operates normally and to this day I have no idea what happens that makes it start operating automatically. Strange!
The other weird thing is that Eudora is now asking to be registered on the iMac. There is probably some reasonable explanation, but heck if I know what it is.