Hi!

My stepdaughter runs a blow dryer in her room and when she does, my APC
unit
makes a humming buzz sound for as long as the dryer is on.

It's probably nothing to worry about. I had a PS/2 Model 80 whose power
supply made a noticeable buzzing noise every time the power floor cleaner
attachment was used on a household vacuum.

What you are probably hearing is the vibration of a transformer. I don't
know specifically about the Back-UPS Pro models, but the Smart UPS and Back
UPS RS models have voltage correction circuits built into them. These can
adjust high or low line voltage without going to battery. Your unit could be
doing this. If it is, you won't hear any beeping. The only sign of it is an
entry in the PowerChute software--if you are using that and have a version
that keeps an event log. (PowerChute Plus and the APC network management
cards (only for the Smart-UPS) do have an event log. I don't know about
PowerChute Personal or Business editions.)

I don't think you'll find that any damage is happening to the UPS or your
computer. However, you really should try to ground the UPS somehow. For its
internal surge protection to be effective, you may have to do so.

William