The converter getting warm is good, that tells you that the 120 is getting to at least the breaker for the converters power supply. You didn't mention if there was any 12VDC from the converter, (you will have to disconnect one of the battery
leads to conform) but I suspect there is.
Depending on how Parkliner wired the box, you should have at least three breakers, 1. A main breaker
2. A breaker for the converter itself
3. At least one or more breakers for 120VAC loads.
But yours may be entirely different from this scheme.
If you have DC you can usually eliminate the first 2 and it's time to get either a 120 VAC test light or a meter out and find out where the 120 VAC stops.
1. A bad breaker. Are you switching them OFF then ON?
2. A wire to the AC outlets has come loose from the breaker or a down steam wire nut has come loose
3. A tripped Ground Fault detector
If you don't feel comfortable troubleshooting 120VAC you can unplug the power cable and remove the front cover of the power chassis and at least inspect for loose wires etc.
BTW: Those 30 amp fuses are usually the in the reverse current protection circuit between the battery
and the converter.
And again, as a mentioned, he AC is separate from the DC and all the power chassis really does for the AC power is provide a mounting place for the breakers. If someone tells you that the converter is bad, be sure to get a second opinion.