Bushfiva is spot on with his last post!
I have actually seen it in a corporate environment, where all the servers were on UPS, but none of the networking equipment (switches and routers). Power went down for 10 secs or so, servers and data were fine, but the comms were knocked out for nearly a day even after the power came back.
Hardly anyone knew there had been a power cut, as almost everybody had a laptop. Everyone thought the lights had just been switched off, until the complaints started.
Fortunately I was just an observer of the event, and responsible neither for the situation nor the solution. But I did learn a lesson that day!
As an aside, a laptop with its built-in 3-hour (ish!!) battery would be a very appropriate desktop replacement in your situation, Feline!
SD