Try the Voltec 600 watt pure sign inverter which costs about $260. It needs to be installed as close to the batteries as possible. Then run an extension cord from it to your flat screen. Works best with two six volt batteries in series so they say. More that enough power to run your flat screen and sat receiver.
Of course there is but you will lose power. That's why the Inverter has to be close to the batteries. You will want the same voltage coming out of your batteries applied to your TV. Don't know your floor plan but you could mount it inside the forward cabin somewhere.
Only if its mounted outside. You don't want to do that. The idea is to mount it inside as far forward as possible. Best to have it professionally done by your dealer.