It sounds like a battery problem.
To test the converter, disconnect the battery (COMPLETELY) from the battery cables. Plug the trailer into shore power and use a multimeter to check the voltage output at the battery cable terminals. You should have 13.6 VDC. If you do, the converter is working and you need to focus on the battery. Take it to an auto parts store and have them check the battery by load testing it.
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John
2015 F250 6.7l 4x4
2014 Cougar X Lite 27RKS
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