The new CPU arrived from NewEgg. It, and the motherboard and memory pulled from Siobhan's computer, into the server case, worked fine. There was a brief period I thought the video was screwed up, but it turns out it's the monitor I was using for testing that's screwed up(!).
However, it wouldn't boot into Windows; at the moment when Windows would clear the "Windows XP" screen with the progress bar, and into a blue background, the monitor would go to "signal out of range". Oddly, this happened even booting into Safe Mode. Booting into "Enable VGA" would let it come up only to an error message saying I couldn't log in because key Windows components were missing.
I dug up my Windows XP disc but was unable to figure out how to start an automated recovery, only the bare recovery console which is no help when Windows didn't tell me which components were missing. Eventually I did a complete Windows reinstall, then added in NT Backup so I could restore my latest full backup (including system state). That ran overnight.
As of this morning, when I only had a few minutes to look at it, Windows would boot up to the same point (where the background goes blue) and then reboot. Same thing in Safe Mode. The boot menu isn't offering me "Enable VGA" as an option now.
I also noticed that Windows didn't offer me the option of installing Windows onto the secondary drive. The list of drives it offered was the C: drive (where Windows lived before) and the D: drive (my external USB backup drive), but not the E: drive (the 250G "media library" drive where all my music, video, etc. live). I may have to check BIOS to see if it sees that drive, and/or open the box up and see if a cable got loose on that drive. Even if it did, though, that shouldn't be responsible for any problems in Windows since that drive was always only a data drive, not a system drive.
I'll work on it more tonight or tomorrow, but I think I'm going to have to do a complete reinstall of Windows, and all the software that ran on it. Just wonderful. Like I've got nothing else to do with my time.