All depends on who wired the inverter. It may only supply power to the outlet on the inverter. Or to one outlet where the TV is.
May never have been intended to power all outlets in the unit.
PLEASE do not send questions via Private Message, my inbox fills up too quickly. Post questions in the forum as a new thread so that other users can benefit from the answers. Use Private Messages for sensitive information only (VIN, Contact info or things you do not want the public to see).