Here's a suggestion that I received from APC tech support:
Do a "brain-dead reset" (their terminology, not mine).
Unplug the unit (and all devices connected to it).
Disconnect the battery (one terminal will do).
Press and hold the power button for 20-30 seconds.
That's all there is to it! Can't guarantee that it'll work for your problem, but it worked for me, and I had a similar-sounding problem.