OK Hiii,
The converter fan won't run unless it is needed. I almost never hear any of mine.
Do it like this....
Get tape and mark every cable that is on one battery terminal. If you only have black tape, use it to make a flag on every wire on the negative connection.
Now, disconnect the battery.
Connect shore power.
Measure the battery (terminal) voltage.
Measure the voltage at the converter terminals.
The battery (if charged) should be 12.6 (it better be more than 12.0).
The converter (looks like a PD91XX could be 13.6 to 14.4.
Now, Come back and tell us what you found.
While you are waiting, clean all the wire terminals and check for the wire connection to be sound.
Matt