Well, this afternoon the computer repair guy returned and fixed the computer in about 15 minutes. The noise was gone after he replaced the power supply unit, the fan of which was the source of the mini-helicopter noise.
Obviously, this was a case of extraterrestrial invasion.
Seriously, though, once we got past all of the stuff about software checking, the repair was very quick. It turns out you can’t check the condition of the power supply unit fan with software. The noise problem was solved the old-fashioned way.