[RMcNeal]

Fridge not running could be the battery was already dead, or the disconnect for the inverter was off (disconnected), the inverter itself was turned off, or the GFCI on the inverter was tripped.
I would start at the battery. Once good, check to make sure the disconnect for the fridge is not disconnected. Mine is a round turn style disconnect in the battery compartment on the back wall directly behind the battery box. You can trace the wire through this wall to the inverter in the basement pass through compartment. If it is set on green, then check the inverter. If it's on, you will see numbers on the display for voltage and amperage supplied. There is a push button on the inverter to turn it on/off. If it's on, check the GFCI test/reset buttons on the outlet on the inverter where your fridge is plugged in.
When I first got my unit, the inverter and the disconnect were both bad and had to be replaced under warranty. Fridge worked on shore power, but not on battery.