These issues sound similar to mine.
I'm kind of a new jack to this scene (2007 Rockwood Ultra Lite TT), and I just purchased a 12V battery to hook up in parallel with an existing battery. The cords are faded, so to tell where each one goes was a little tough---especially since there is red/white/black, etc.
So I hooked them up, and I have a key I place in the driver side of the frame to turn it over to battery power. I did it, and it ran great---all except the tv and radio. Everything I was reading was saying that it was reverse polarity (which is very possible), and the 40 amp fuse blew--as well as the 15 amp in the radio.
The problem is now that my TT's lights did come on with the battery power--but quickly began to fade. I also plug into shore power with no luck whatsoever. The microwave beeps on, but the water pump has no juice.
I still have a 40 amp fuse to replace, and then we will see if it is just the battery or the inverter. We are getting ready to drive to Austin tomorrow....so this is not the most exciting news, as everything was working great before the battery hook-up.
I thought I'd lay my story down because it sounds eerily similar to TheGirls story.
Any advise would be appreciated. Thanks!