Found the problem with Grandma’s PC. The UPS batteries were fully discharged. Apparently it had started making all these noises after last Tuesday’s valley-wide power glitch, which had caused power outages ranging from less than a second to over an hour, depending on the part of the valley you were at. It appears the UPS went on battery power during this time, completely drained them, and never quite recovered. I left everything turned off and let the UPS recharge for about a half-hour and it appears to have gotten over the recharge-hump — Everything seems to be back to normal again.