Update:
Had a couple of days to cool off. Put a new battery in yesterday, removed the old thermal paste from the processor and heat sink, and applied a new layer of goop. Finally got her home today, and after running for several hours the new CMOS battery seems to have taken hold. Had a look in Setup at the POST error messages and noticed an entire page of errors related to the old battery. How the tech could have overlooked something that simple I will never know, but I do have my suspicions.
The system functions - she's alive!
For the time being, anyway. I'll power it down overnight to verify whether the battery really was the only problem.
Before deciding on bringing her home I asked my stepdad if he wanted to try to sell it, and hopefully recover some of what he had spent on their new computer. He told me, "It's yours. We would have thrown it out anyway". Not exactly the way I would have preferred coming into a used computer given the circumstances, but I can't really complain, either.
Jan Kyster requested pics and I will have them posted as soon as I get the images uploaded to Flickr, if the interest is still there.
Thank you to everyone who responded earlier. This will be one of the first places I go to when a real project lands in my lap.
