You have clearly lost the converter.. Sounds like your converter and inverter are 2 different boxes.
In most RVs there is a switch, sometimes called a Salesman switch but it is really the battery disconnect, It may be lebeled AUX or USE/STORE or Disconnect, or Well, use your imagination, OFten it is just inside the door about eye level if you are standing on the ground.
On my RV, it failed.. I fixed it, and so far it contiued working.
Now this varies rig to rig,, On mine it's a small rocker, Light weight, just sends power to a solenoid located elsewhere.. When I pressed STORE I clearly heard the CLUNK of the solenoid.. When I pressed USE.. NO CLUNK, I could not re-connect.. (I will tell you how to fix if you need it).
Look for this switch
Also, Inverters come in two flavors (By two more) for this post.
Stand Alone and "in-line" in most cases an "In-Line" also charges the batteries IF shore power is present... Alas it can not if no shore power
I have seen mine trip the circuit breaker... And mine is plugged in and I've accidently pulled the plug a few times (And pulled it on purpose a few times too, most recently this week). Many are built into the power panel.. And all of them have fuses too.
Home is where I park it!