Bug or hardware failure

[Alvin]

A week ago, a server of mine suddenly started to halt on random moments. Blank 
screen, no input. Drives and memory where fine. I needed frequent reboots to 
be able to finally start the machine (always that blank screen)
Nothing in the logs hours before a sudden crash, nothing in /var/crash.

After a BIOS upgrade, the only message I got after a flash of grub was:
PANIC: early exception 08 rip 246:10 error ffffffff810356e6 cr2 0
(Older kernel gives same message.)

A replacement board showed the same error on boot, so unless both boards are 
faulty, a software error is more likely.

I had more success getting the system to boot with 'Intel Trusted Execution' 
disabled.

So, how would you debug a situation like this?