John: I'm afraid I don't really know how to help, but this sounds very strange to me. I think that the problem must be specific to this box. In the 5 years I've been running Linux (first Slackware, then Debian), the only program that has ever brought down the whole system has been Corel's Wordperfect (hate that program). And that happened just once.
Maybe it's bad memory? There's a utility called memtest in the sysutils package that might be able to detect it. It can detect things that the BIOS memory-check can't, but there are also a lot of memory problems that it won't detect at all. A much more thorough test is memtest86 in the hwtools package---a program that you boot into via floppy. That gives your memory a real going-over, Jim