The battery should not have anything to do with the 120V system.
However you need the 120V system so the Magnetek 6300 converter can
charge the battery.  You should look for tripped 120V circuit breakers.
There should be a 120V breaker panel somewhere usually near the Magnetek
12V fuse panel. Make sure the main circuit breakers are not tripped.  If
the main circuit breakers are not tripped in the 120V panel then you
have a problem between the 120V breaker panel and the 120V shore power
plug.   If you are not comfortable working with electricity you should
take it to an RV dealer.  RV's 120V systems are not wired exactly the
same as house wiring at the panel.  The neutral and grounds are wired
differently then in a house.

The 12V system and 120V system are separate.  When not connected to
shore power your 12V system works off the battery and you have no 120V
power.  When connected to shore power the 120V system supplies power to
the converter which changes it to 12V power and your 12V systems run off
of the converter, the converter also charges the battery.  All your 120V
systems then work too.  Stuff like microwaves, TV's etc.  You have 12V
when hooked to the tow vehicle because the tow vehicle is supplying the
12V power through the connector to the battery, trying to keep the
battery charged while towing.  Since the 12V is there at the battery the
12V systems will work.

Take care and Happy Campin...