Since it seemingly can't see an NIC, have you tried to disable it at BIOS level?
Some old timing circuits used to use heat and could easily be accurate within a minute out of 30, but not to a second out of 30 minuets.
My old HP shut down due to the capacitors adjacent to the CPU. It was a fairly accurate timing, but not exact. However, it might be worth a look at those to see if any are oozing. Usually 5 years old before that happens.
You might also look at core temps and see if one misbehaves, but again, accurate to a second in 30 minutes it wouldn't be.
It sounds like you've asked yourself what should comply with what at 30 mins - and does not.
Despite it seeming independent of OS, I'd still boot with a non-windows OS just to make sure.