The furnace problem sounds like a fouled or broken sail switch, especially if your trailer is new (they get fouled from all the sawdust Keystone leaves in the rig).
(
Speak of the devil...)
The TV amplifier wall plate is available from lots of internet RV parts vendors for about $25 ($15 if you don't need the cigarette-lighter socket), and is relatively easy to replace (it's all spade connectors).