Being 12 VDC the outlet is fused rather than on a circuit breaker.
First thing to do is to check to see if the fuse is blown. Locate your convertor panel. It probably looks like this:
Along the top edge of the panel there are two little black plastic thingies that have a slot in them. They are latches to hold the panel closed. Stick a coin or a screwdriver in the slot and rotate 90 degrees. The upper panel should then swing down and then it should look like this:
On the right hand side there are some automotive fuses. Just below the fuses on the lablel there should be a list of which fuse is what. Check them to see if one is blown. They're easy to check, just pull them out and look at them - if it's blown, it's plainly visible.
Second, presuming that the fuses are ok, just check the AC breakers on the left side of the panel to make sure they're properly set. The breakers should not affect the DC side of things, but it doesn't hurt to check them while you have the panel open.
I went to the Winegard website and looked up the outlet. (Here's a link to the installation manual for that outlet: http://www.winegard.com/kbase/upload/2451808.pdf
) In that manual, I found this information: This unit is equipped with a polyswitch, (current limiting device), which will shut down +12 VDC if there is a direct short between antenna and power supply. Green indicator light will not light. Once short is eliminated, device will reset itself.
So it is possible that there may have been a short in the outlet when you plugged in the inverter. Has the outlet device reset itself and is there 12 VDC available at the outlet? You may want to try it again, and see if the 12VDC is absent from the plug afterwards.
One other thought.... I believe that inverters are voltage sensitive meaning that if there isn't sufficient DC voltage present, the inverter won't function. So it is probably a good idea to make sure the battery is fully charged.
Also, check the wattage on the TV. If the TV needs more than 100 watts, then the inverter probably won't work properly.
Last, it would be helpful to test the inverter to make sure it is OK. Perhaps plug it into your car's cigarette lighter and see if it will run the TV.