I was going to write and tell you some anecdotal tales about a former repair-anything-electronic colleague of mine who instinctively knew never to touch UPSs without specialist repair facilities. Instead, for fear of waffling too much, I'll try and give you a couple of practical tips based upon what he told me

Although they run from 12/24/36 volts and may seem fairly harmless they can be very dangerous.

Wear face & eye protection
The current carrying capacity on the switching side of a UPS is very high so even though it's a relatively low voltage there is a LOT of electrical energy available. If, during your investigations, something goes further wrong there could be a very big bang and you could end up with bits of exploded power transistor and molten metal in your face/eyes.

I know you probably run 110v applicances so this is less of a danger to you than it would be to me (240v); there is almost certainly no automatic shutdown in the event of an accidental earth leakage on the mains side.