Well, last night I was still busy copying stuff, so I didn't report exactly what I was up to. I copied any files of any importance onto the new hard disk I bought for my G5, then removed that drive so that Apple would be working with the warranted drive, and I would also have a backup of everything.
I also copied all files I expected I might want access to in the next week or two (most of my home directory) to my iPod. I then copied the 16.5 GB I placed on it onto my PowerBook, which is now serving as my primary system. (Thanks to .Mac sync, my PowerBook is usually already well sync'ed with the PowerMac, but I don't keep everything on it.) The only things I needed to copy onto it were my documents, photos and music. E-mail, being IMAP-based, was already there, and .Mac takes care of bookmarks, contacts and calendar.
I then brought the PB onto my desk and plugged it into my Cinema Display. The system happily woke up from sleep and automatically switched to the maximum 1920×1200 resolution of the display. I could almost forget I wasn't on my G5, if it was not for the fact that things are quieter, and my dock looks itty bitty on this screen (since its size is adjusted for the normal 1024×768 resolution of the 12” PowerBook).
The Apple Store said they weren't sure what was causing the problem: the SATA controller, one of the processors, the logic board as a whole, etc., but they were going to look at it today. Depending on what is needed, they may already have the needed parts in stock. That would be nice!