So... it's not the memory. The memory has passed all tests and I swapped it out when the new memory arrived... Still, I have the problem.
To answer the question as to when do I get the Blue Screen of Death... It might happen immediately or in two hours, or maybe five minutes... it seems random.
An update on the second computer that I tried using... After Mach caused the BSoD, that computer is completely dead. Paperweight dead. Doorstop dead. Dead.
I have put Mach on a third computer, an old, slow, eMachine, it should have a crank on the side, but it did pass the driver test program... No BSoD on it yet, but like I said, the first computer worked for years before there was ever a problem and I'd still like to get it working again.