Measure battery voltage when on shore power. If it is not over 13 volts your converter is not working. It runs on 120 volts to produce 12 volts for charging and 12 volt loads. It will be on one of the AC panel breakers.
One of the handiest tools for diagnosing AC problems is a non-contact voltage detector, (under $20 at Amazon or your local hardware store). With it you can easily touch it against the AC connection into your converter to see if it is getting power.
If it is getting AC power you need to check the output terminals with your 12 volt test light,(under $20 at Amazon and another essential part of your tool kit). If the light doesn't go on and there are no fuses to replace on the converter then the converter is dead.
If the 12 volt test light does go on you have the task of figuring out how it connects to the 12 volt battery looking for a disconnection or bad connection. In particular check the ground connections of the battery and the converter, remove, clean and replace.