I thought (maybe wrongly when I reread his post) that he has the Winegard video switch box which does have the antenna amp supply built in.
If not then he does need to remove the wall plate cover and see if there is 12 volt DC coming in and going out to the antenna.
Following is a picture of the rear of the wall plate. The two unlabeled wires are + and - 12 vdc.
When the button is pushed the LED should light and there should be 12 vdc on the coax connector labeled "Antenna downlead".
Remove the coax and check the center hole in the connector on the pc board for 12 v. This voltage goes through the coax up to the batwing antenna head amplifier.
If the LED does not light, there may be a fuse on the wall plate pc board you can check. There is one on mine.
Note that the unit also acts as a A/B switch. When the button is pushed (LCD on) the coax connector on the front side of the wall plate and the coax connector on the pc board labeled "Set two output" are connected to the bat wing antenna.
When not pushed (LCD off) they are connected to the external cable input in the service bay - labeled "Cable input" in the picture below.