Maj, you've gotten good info on ground loops, but as I indicated in my previous reply, from your description it appears that there can't be a ground loop. For a ground loop to be formed there has to be at least one power connection path to the sub besides the direct connection through its power cord. This could be be through a plugged-in receiver or something connected to the receiver which in turn is plugged in to the wall, such as a player. Neither this nor any other subwoofer connection to the power other than the subwoofer power cord is present, and one connection can't make a loop. There have to be grounds to two areas having different electrical potentials so that the difference in voltage between them causes a small current to flow, with a resulting hum.
No, when the sub is plugged in and turned on, but not connected to any signal source there should be no cone movement or sound audible. The rectifier and filter capacitors in the amplifier power supply section should remove any audible noise coming in through the power cord. Possibly the repair to the sub amp was ineffective, or it's been somehow damaged since then.
As to the sub cable itself(not connected to the receiver at the time?)causing the problem to worsen, this may be reaching, but possibly it's acting as an antenna picking up airborne electrical interference to add to that coming in through the power cord and not being adequately suppressed by the amp power supply section. Tough one!
