The converter does not supply power to the 120 volt outlets and the dc voltage from the converter does not go directly to the inverter but to the batteries. The batteries supply 12 volts dc to the inverter for producing the 120 volts ac.
Do you have GFCI outlets and have you checked them?
Do you have breakers in your breaker box for the inverter? You could have one or two breakers depending on the model of inverter you have. And, have you cycled the breaker/s?
Check for 12 volts from the batteries to the inverter. There is probably a fuse on the 12 volts from the batteries to the inverter and if you don't have 12 volts at the inverter it needs to be checked. On my coach this is a large 300 amp fuse. There may well be breakers on the inverter itself that may need to be reset by pressing on them.
Inverters usually have a secondary breaker box for the output of the inverter. Sometimes the manufacturers hide them pretty well. I found mine by accident. If you aren't getting 120 volts when on shore power this is a good candidate for the problem.
Also, the 120 volt shore power goes from your breaker box to the inverter and then out to the outlets. There is a transfer switch built into the inverter that switches to allow shore power to pass through and then switches back when you are using the batteries to produce 120 volts through the inverter. This transfer switch may have failed.