If the battery cutoff key (Red) can be removed then you have battery cutoff in off position . Turn key to other position..
Your gonna need a multi meter and remove battery terminal from battery and measure battery voltage with no shore power.
Leaving battery disconnected plug shore power in and measure voltage output at removed battery cables...
You should see 13.4 to 13.8 volts DC on those leads...
And a fully charged 12 volt battery should read within specs on this link
https://www.rvtechlibrary.com/battery/bat_volts.php