If the battery tests good and everything works on 120 v shore power, the connection between the battery and inverter is the area to search. It could be a bad connection at the battery or ground, a tripped or blown fuse or circuit breaker, etc. Use a test light or multimeter and check for power at every place you can between those points. It wouldn't hurt to unclamp the cables at the battery, clean them and reconnect them. Do the same at the ground cable connection.