BuddaBINGO!
It was the memory.
The issue I was having was that I was ripping music on this PC (to save me the hassle of burning to disc and copy/paste-ing all the files). I had done this before, but was using a different format and version of the programs, and THIS time, each and every time, I was getting BSOD's and mysterious reboots when LAME was encoding.
First thing I checked were mobo settings, and this one has no settings other than CAS latency settings, which had no effect. Two of the LAME dev's recommended testing the mobo and memory, and one also mentioned Prime95.
Prime95 brought up errors, but that program is non-specific. It alerts to problems with the CPU, RAM, cache, & mobo, but it doesn't report which one, unless there's a forum I don't know about where you report your findings and they interpret them for you.
I had heard of Sandra, but was under the impression that it was for sale, and more money than I was willing to spend just to find out if this old system was shot.
I'm willing to bet that testing old systems before putting them together for MAME or jukebox purposes is something folks would like to do, so if there's other suggestions too, we can point to this thread.