Looking at the schematics of some old models of BackUPS I found online the output relay needs to be powered in order to supply output from mains. Combine this w

Looking at the schematics of some old models of BackUPS I found online the output relay needs to be powered in order to supply output from mains. Combine this with slightly funky internal power topology where +12V for internal logic comes mostly directly from the battery and it is pretty clear why battery with shorted cell(s) causes the thing to completely shutdown (probably even due to thermal shutdown of the LM317 in charging circuitry).