But I am still a bit puzzled why my computer lost power and the screens went black, when I still had electricity at the office.
This UPS typically switches to battery backup mode when voltage drops so low that incandescent bulbs dim significantly. That is what it should do. Temporary power. However these things are made so cheaply as to be fooled even by electrical noise. In your case, its battery was defective. If AC line noise caused the APC to switch to batteries, then batteries could not provide sufficient power to the computer.
A resulting lockout was cleared by pressing its reset button. Does not matter if sufficient AC power was incoming. That UPS had completely disconnected from AC. And then locked because its battery was nearly dead.
Plug a laser printer directly into the same duplex receptacle that powered the UPS and computer. Electrically same as when plugged into the UPS 'surge protected' outlets. Power demands, as demonstrated by Gene's numbers, are well below what would cause problems on properly wired circuits.
