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Hi my name is Robert.....
Do you happen to have the make and model of the power converter?
It sounds to me if you are plugged in you have an issue with the power converter, it should be charging the battery. Sometimes on the cable from the converter to battery you will find an auto breaker, as a general rule they like to stick them 18" from the battery and could be on the frame. Most have a small tab that pops out when they trip but some are thermal. IF you see any I would check the voltage on each post, it should be close. Sometimes the breakers can get corroded.
IF it is not an auto breaker issue then it sounds like the converter, the converter will be part on the main breaker/fuse panel or stand alone and plug into an outlet. On the stand alone style they can be close to the breaker panel under the fridge, stove etc. IF you know the make and model I should be able to send some info for testing... Robert