I'm afraid my motherboard must be toast. I've tried everything I can think of, and everything you all here have suggested. I'm out of thoughts on what to try next.
(1) New power supply
(2) New memory modules
(3) Cleaned off old CPU thermal paste and applied new
(4) Checked all fans for proper operation
(5) Cleaned out all dust from inside (heat sinks especially)
(6) Inspected motherboard for bulging caps
(7) Disconnected all peripheral components that I could: All hard drives, the SSD, one of the two optical drives. The only thing left connected is the primary optical drive so I have something to boot from.
(8) Booted with a Linux LiveCD (different distro than was installed on the SSD for normal boots).
And I still have unexpected shutdowns. And they are now more frequent than they used to be. System is not hot, all heat sinks are cool to the touch when it shuts down.
The system is about as bare bones as I can make it: Motherboard, CPU, memory, power supply, one SATA optical disk drive, USB keyboard, USB mouse, monitor connected to DVI output, booted from optical disk. No GPU installed - I am using onboard graphics. I do still have one PCIe x1 card installed ... to provide USB 3.0 (which is fully functional). I suppose I could pull that out too, but I don't really see the need.
