I just went through this. Your 12V converter appears to have died. Your lights run on 12 volts, and most of your appliance run on 120. Your converter takes the 120 volt supply, converts it to 12 volts and uses this to charge the batteries. When it goes out, the batteries won't charge and the lights dim and finally go dark. When you plug in your TV, the 12 volts is supplied via your TV's charging system and the batteries in the trailer charge up again.
There are a couple things you can check:
1. Most converters have fuses that protect them if you should happen to hook the batteries up for even a second with the wrong polarity. Check the fuses and make sure they aren't bad.
2. Carefully pull the converter out of the housing and verify whether it's putting out at least 12 volts with a volt meter when you are connected to shore power or your generator. Be extremely cautious doing this so you don't get electrocuted by the 120 volt side. If the fuses are good, and you have no output from the converter, a new converter is in order.
Send me a private message if you want more guidance.
