[Sopater]

They would have needed to gain physical access to the machine and installed some sort of remote power switch, I assume.

I believe that if someone can access the BIOS, they can set the computer to come on automatically at a set time every day if they like.

[Buckeye McFrog]

Happened to us years ago (dial-up modem days). Got hacked and someone programmed the machine to dial some number in Africa at 4AM and begin forwarding emails. Little problem in that the early morning one-hour call to Senegal stuck out like a sore thumb on our phone bill.