The first step is to get a hairdryer out, plug it into the back of the APC UPS unit. Unplug all other outlets being used by the unit, then turn on hairdryer. Remove cord from wall outlet, if unit continues to work it should between 3-4 minutes before the hairdryer stops working. Anytime less than that its safe to say you need a UPS battery replacement.
Come back, more details to come