Electrical-sat controller and bed inflate-no power

Both of those circuits are 120 volt circuits so you need to make sure that BOTH legs of the shore pedestal are hot and check to see if you have another GFI in a basement compartment. It is always a good idea to reset all circuit breakers rather then to rely on a visual inspection looking for one that has tripped.
On some inverters there are three circuit breakers. One for each leg and one for the charger portion. These are usually on the inverter itself.