Make and model of refer would help.
Since it is getting power to the display panel the refer is getting power.
Disconnected from shore power.
Disconnect battery.
Locate the battery fuse in the 12 Volt DC panel.
Connect battery up.
Use volt meter to check for 12 volts DC to bat fuse holder.
No power? Check fuse or circuit breaker near the battery. Could be in battery box, along frame rail under front of trailer or in junction box where the Battery cable, umbilical cord and trailer wiring comes together.
Another way disconnect from shore power.
Disconnect battery.
Plug into shore power. Check for 12 volts DC in 12 power distribution panel.
No power. Replace or test, do not look, at reverse polarity fuses.
Post make and model of converter.