The "button" is a power inserter for the amplifier. If you disconnect the coax (may need to pull the panel with the button to do so). you can then use a multimeter to make sure the center conductor and outer braiding are not shorted out. You can also pull the antenna lose from the roof, and verify integrity of the coax with a multimeter. Would be a good opportunity to install a nice new antenna, like a Winegard omnidirectional Air 360+ antenna with HDTV & Internet or something.
All that said, I've seen shorted coax (little stray wire in F-connector), wires not connected properly - the "little button" plate has three connections that need to have correct coax connected in the correct place and of course bad amps in the antenna itself.
Pulling the antenna lose from the roof may seem extreme, but it will give you opportunity to do proper troubleshooting. NOTE: Use DICOR self leveling sealer when antenna is reinstalled (has picture of a bald guy on the tube).
OK, I've rambled enough, gonna go get another cup of coffee . . . Hope this helps a little.
Rich, MCPO, USN, Ret.
RV Service Tech
RAM pulling 2021 GS TT