Your converter is essentially a big battery charger - only works when it's plugged into shore power and sends power to your DC distribution system and your rigs house batteries. When you disconnect from shore power you converter no longer works.
Your problem isn't related to converter but the battery. They maybe dead or one of the fuses between the battery and the DC distribution panel maybe blown. Check the voltage on the battery or have the battery tested for free at any auto parts/tire outlet. Many rigs have an auto reset circuit breaker that sits near the house battery - when that goes toes up it essentially disconnects the battery from the rig - they are inexpensive. They don't look like normal fuse or breaker so use Google to get a pic. Lastly - many rigs have battery disconnect switches - some manual, some toggle, == make sure that those are set in the correct position.