I've got the exact same problem. Mine is JBL system. It's not that old, maybe 4 years max. It is an auto detect on off system and it's self powered and plugs right into the wall. I recently moved about 2.5 months ago and one morning out of the blue i heard those big "THUMP" and them "zzzzzZZZZZ". Scared the crap out of me, i thought a bomb was about to go off somewhere. I was sleeping and it woke me up. I tried to see if it was interference somewhere so i disconnected the signal cable that was going to it. The sound was still there. So i unplugged it and plugged it back in. The sounds seemed to go away. Funny thing was, the "auto detect feature". The subwoofer was still in the "off" indication. The LED lights on the front were red. They light green when it powers up and receives a signal.
Then the next day i come home and hear a "thump thump thump thump" coming from upstairs. I went upstairs and surely enough, it was the subwoofer. Same thing. I touched the subwoofer speaker itself and it stopped. It was kind of like resonating. I let go and it started again. It was wierd. So for now, it's just disconnected. I hope there isn't something broken in there. That thing was expensive.