Well i had exactly the same problem, my sub turned off right away when i turned the whole thing on. Well i opened the subwoofer and was trying to find out something unusual, i took out, i believe, internal amp, well, whatever that thing is, under the lid. Which one is screwed with 6 copper screws, so you unscrew those screws, lift that lid and that whole board comes out. On that board i find something like burn around one of the parts.
http://www.flickr.com/photos/28004328@N04/3333561417/in/photostream/
you can see it in the pick, the part q2902, then i contacted JVC. At the beginning they said i need to take the whole thing to service center and so on. But later i made them to tell me what kind of part that is, so here :
http://www.jvcservice.com/store/ProductDetail.asp?Part=KTC3199/GL/-Tbought soldering gun in home depot for $15, returned after i was done. And that is it, just have to replace it, but total cost only $12 ($5 part +$7 shipping)
