make model # of inverter
good possibility that you have a Combo inverter/charger
shore power pass thru is built into the combo unit
meaning replacing the converter means installing a "replacement" unit that is also a combo unit
try this test
get a long 15amp extension cord, unplug coach from shore power unplug TV and media from internal outlets, plug into the extension cord
if this problem has existed since NEW, then the combo charger is faulty or very likely has a loose ground which allows interference to be on the 120v pass thru