Has light but no sound

Auto-off will be a software issue, so no, you can't turn it off. Send it back as a warranty repair. They have a 1, 3, or 5 year warranty. Look at the the support page. Also shows factory repair.

SUNFIRE True Subwoofer EQ 12 Signature TS EQ12

You can prove the sub pre-output works by running an RCA cable from it to the input of a tape deck, TV or any other device that accepts Line In and will either display it or play it. Test it on VERY LOW volume at the receiving device.

Different sub pre-out cable?

that's just likely a dirty potentiometer. (the circuit under the knob)

You could find the manual here:

http://www.retrevo.com/samples/Sunfire-Subwoofer-manuals.html

I think it will be most likely a semi-conductor device that is overheating. Probably the main amp device. Subs are basically mono amplifiers.

It sounds like you are describing an earth loop problem. I won't go into detail in this post, but try an isolation test first. disconnect everything from the reciever except the sub and try connecting say a BATTERY powered mp3 player or cd player to minimise connections to the electrical mains earth. you could also isolate things by taking your sub to a friend's house and trying it on their system.
If it is an earth loop use a process of elimination to find out which two pieces of equipment causes the earth loop. then apply filtering.
you can buy earth loop isolation transformers for about AU$26 and I've used one on my sub myself. Theyhave RCA (phono)plugs on each end and they connect inline with the signal cable to the sub amp.

as for the thumping sound it might be the speaker protection circuitry cutting off the amp to protect the subwoofer speaker from damaged. This might be triggered if the earth loop sound is causing the sub amp to overload and clip.

Failing this there might be a dried out overheated electro capacitor in the amp circuit causing the hum. Hav a chat to your local electronics person, who should be able to spot it!
Hope this puts you on the right track
Happy Hunting!

It sounds like the internal amp has failed. You could look inside and see if any of the main semiconductors has failed or blown apart!

big red
if its that old then you should keep it look for spare parts from other subs just make sure it is worth it

You either ripped your voice coil, or you have something jumping around inside (Screw, nail, etc.). You can tell of a blown speaker by pressing straight in, and if you hear a rubbing noise, then your speaker has disconnected from your voice coil. Mickey mouse jobs include Krazy Glue, but It's touch and go

send this baby to the manufacturer, great service at fair prices...they will often repair for free