Around noon, an hour and a half after I'd given up and turned to my laptop, my work computer switched itself on, all on its own. I leaned over to answer the phone, and when I hung up, the login screen was smiling expectantly at me.
All I can think is that there is a loose contact somewhere, and the rising temperature over the course of the morning caused it to make contact again. We had extreme temperature fluctuations today because the heating had broken down, but my office faces due south and has full length sash windows, so the sun heated the room by a good few degrees, as
parrot_knight can testify.
I did however achieve a first today: in addition to swooping down on me with ill-timed passive-aggressive advice, the Female Twin asked my advice on an editorial point today! I answered, too.