Welcome to HTF. Here is a link that helps with troubleshooting electrical issues associated with the battery.
Trailer Wiring Diagrams | etrailer.com
You should start by checking the output voltage from your TV trailer connector to make sure you have the right output voltage being supplied to the trailer. If not then it could be a blown fuse as poprichie suggested. If you have the power output from the TV connection, then next check at the battery terminals in the trailer to make sure you have approx. 13Vdc with your TV running, this would indicate adequate voltage to charge the battery. Hope this helps.