This is just a possibility, but are you sure the WiFi on the TV is turned on? Some of them have an option where the WiFi and/or its search function can be turned off/disabled. I just though that maybe, for whatever reason, one of those two things may be turned off, or may have been turned off, without you being aware of it. Also, you may have to force the TV to search for available WiFi connections again.
If it's on, the TV should be able to see at least the 2.4Ghz WiFi, as that's the one of the two with the better range, plus the one that nearly all WiFi devices can connect to, while many devices to this day still can't utilize 5Ghz WiFi.
If it still can't see the network after forcing it to search for it, and though I don't know if it will help, one option is to unplug the TV for a short amount of time, then plug it back in. This may help to "reset" it somewhat, sort of like a computer clearing its DNS cache when it's shut down or restarted. You could also do the same with the HughesNet modem, though, if your phone is seeing the WiFi network, it's doubtful that it will make any difference, as the phone seeing the network means that the modem is broadcasting the signal. Still, it won't hurt to try. For the modem, unplug it from the wall outlet or the power brick (but NOT from the back of the modem), wait at least a minute, then plug the modem back in. Then wait at least five minutes for the modem to be fully back up, then try the search for the WiFi again with your TV. If your phone can connect to the network at this point, it's definitely broadcasting from the modem.