Well, DRAT and DOUBLE drat. Now I know what the VCORE VOLTAGE error is on the hardware monitor, which is what we were getting when we tried to boot our desktop PC.
The motherboard is toast. As the PC in question is from 2001, motherboards compatible with it stopped being made years ago. The fellow at the Geek Squad said that even if it were possible to locate a replacement motherboard, it'd cost so much that it would be more cost-effective to just replace the entire machine.
So we'll be looking through ads for a bit, to find out what's out there in desktop PCs these days.
On the one hand, DOGGONE IT, we really don't need to be hit with another expense after this year of Car Repair Bills from Hell and a jaw-droppingly high veterinary bill. On the other hand, we got eight good years out of this computer, so I really can't gripe tooooo loudly.
Still... phooey. What crummy timing for something else to break. Oh, well. Life goes on.