Well, I installed the new hard drive to replace the one that had failed and the computer still failed to boot into BIOS, even when I disconnected all of the drives. Swapping the video card didn't help either. I could have started pulling RAM modules, but I decided it was time to cut my losses.
Thus, I have gone to NewEgg and ordered a new motherboard, a faster processor, new DRAM, a couple of new hard drives, a new SATA DVD burner, and a copy of Windows 7 Professional. They'll go into the old case to join the nice new power supply when they arrive and then I'll have several joyous hours reinstalling the world. Fortunately, "the world" on the studio machine is actually a pretty small set of programs.
And the _audio directory. It's now being backed up from the working hard drive to the NAS, as I've taken it up to the office and plugged it into a little Rosewill USB dock that I got for free when I ordered something from NewEgg a while back. Another 100 minutes or so and everything should be backed up.
The other hard drive, when plugged into the USB dock, causes the dock to shut down. This is a familiar story.
And that is why all of my important machines have mirrored hard drives. :)