So, the question becomes, what's wrong with it? It could be a badly corrupted Win2k install certainly possible. Could be a flaky power supply, but I don't buy that because it's a clean warm-reset not a 'glitch and power back up'. Worst case is a motherboard that's starting to go bad. I tried dropping the C: drive into a spare PC and got a BSOD (inaccessible boot device), to which I thought "WTF? These are both vanilla PCs with plain-Jane IDE controllers, this *should* work". Bah.
After a couple of hours of testing I'm on plan B: pull out both original disk drives and the known-to-be-bad CD/RW, install the new hard disk and CD/RW and build a fresh install of Win2k. If it gets all the way through installation and applying SP4, I can probably rule out a hardware problem. The next step after that will be stuffing the original disks back in in hopes of extracting their data. This certainly rates as the most vexing PC problem I've tackled in some time.
In other news, I visited my sister's place this evening to have a look-see at how her phone lines are setup and where in the basement I can set up Alpha and Beta. The phone situation looks good the DSL modem kit even came with a DSL line filter for wall phones, and there's a disused phone jack poking up into a room right above where I'll put the servers. I'll hijack the line and thus will hopefully avoid having to run any new cable. There's even power nearby. I plan on doing the installation this weekend.