If your UPS did not maintain the running PC then it has failed badly.
The lead-acid batteries are supposed to be replaced every few years (recommended length=2-4 yrs
). I replace them usually after the alarm starts to go off signally it fails its power up test. My batteries last usually 3-4 years before a waring light comes on. I usually ignore it until the audible alert starts up. But if I lived in an area with frequent blackouts and needed more than just a couple of minutes and enough time to save and shutdown I would replace sooner.
The fact that you didn't even receive an alert when the power came back on may mean the problem was with the UPS unit and not the battery. Did you do "the test" upon initial installations? Otherwise how do you know your UPS ever worked? "The test" = power up the PC and equipment plugged into the UPS then yank the cord out of the wall. It should wail but the PC should never miss a beat.
Keeping the PC from losing work or allowing automated shutting down during a brief loss of power is one primary purpose of a UPS, but its other is to prevent over-voltage and under-voltage (both common in US electric grid) from reaching the PC and accessories (i.e, clean up power).