Humming and/or Battery Drain with SONY CDX-F7000

I bought a used car with the SONY CFX-F7000 CD changer/radio/etc. and it worked fine for a while.  Then, when it was parked for a few weeks without being driven, the battery had totally drained. So I bought a new battery; that one drained as well as the car sat there.  Now, I'm trying to fix this all, but when I push ANY of the buttons on the faceplate when it is attached to the unit, I get a 30-sec. loud humming sound coming from the big-ass speaker in the rear of the car.  I can suffer with the humming sound for a few seconds, but I'm afraid it's going to drain the battery again.  So ... there are two problems ... can anyone help with either one???