[Richard Crowley]

"D" wrote ...
The hum is from speakers, not from the case. Yes, either of the
headsets work OK on another computer.

Then it is possible that the sound card has a problem.
Since the sound card feeds power into the microphone in
the handset, the filter capacitor on the microphone power
may have a problem that is letting 50Hz hum get injected
into whatever microphone is connected. You would not
hear this unless a microphone was connected. Since the
headsets work OK on another computer, that casts the
suspicion back on the sound card.