Another idea....
Depending on the age of the BIOS, there may be an option in Power Management to alter the PC's behaviour after a Power Loss.
My machines offer to :
1. Power Off
2. Power On
3. Resume Previous State.
I had a power outage in the small hours a few days ago. After it was restored, the machine that should have remained OFF came ON and the machines that should have powered ON under a Scheduler Setting for Back-Up purposes stayed OFF!
Now they all Resume Previous State.
Could be something here for this enigmatic case.