The motor is separate from the spindle that turns the floppy disk. The belt goes from the motor to the spindle that turns the disk. If the disk spindle is slightly sticking, it will cause a whirring sound, because the belt is slipping ever so slightly. You can hear a similar sound with a car's fan belt, if something like the AC pump, smog pump or water pump are starting to have lubrication/worn bearing issues. My Mustang GT was making that same kind of noise, until the smog pump finally stopped turning, the belt started smoking and finally snapped. I only brought that up, because he had said that he'd heard a whirring noise.
If it is a tantalum capacitor that gave out, it would definitely smoke like he described. He should see a burnt capacitor if that did happen.
https://www.reliabilityanalysislab.c...talumCaps.html