I did not use the Toshiba factory restore disc, I used a fresh clean known-good copy of the OEM versions of Windows, including XP SP3, Vista 32 Bit, and Windows 7 64-Bit. (It originally came with Vista 32) It crashes with ALL of them. Likewise, various distros of Linux crash with random kernel panics. It's DEFINITELY a hardware problem with the motherboard, I'm guessing either in the chipset, or perhaps the L3 cache on the motherboard. The bios does not provide a way to turn off the L3 cache, but I've run Memtest for days without any problems. It's not the processor, I changed it and carefully cleaned the new one and the heatsink and applied fresh thermal paste, the fan runs fine, and the CPU temp generally stays under 60Â° C or less. And as I said in my original post, all the various diagnostic utils from web searches either crashed themselves, or didn't report any errors. I've tried the latest, and older, versions of the bios, and drivers.
It's just as likely to crash sitting at the desktop as it is running a program. Another weird thing is that it tends to crash shortly after a cold boot, and the longer it runs, the more reliable it gets. I also booted MS-DOS 6.2 from a flash drive, and sitting at the A:> prompt it never crashes, but running dos based diag utils will eventually make it crash.
I have a new motherboard now for it, and it is working great, so it's kind of a moot point. But for future reference I would like to know of a decent diagnostic utility, one that tests the various functions of the motherboard chipset (SouthBridge, NorthBridge, London Bridge...). I saved the old motherboard BTW. I'm not a newbie, I've been doing this for 30 years, and I happen to think I'm pretty darn good at it, so that is why I am so very frustrated that I can't seem to put my finger on this problem. As my father used to say when working on a temperamental piece of machinery, "This has aroused my competitive spirit!"