We are talking 110v from the generator - so store/use switch has nothing to do with it (that only affects the 12v side of things... including fridge control panel which he said works.)
Breaker on the generator may be an issue as TurnerFam posted - one leg coming out may have tripped disabling half...
If not...
The microwave should work on generator power. If the circuit breaker is ON - sounds like an issue to report... (Had an issue with mine on delivery as well - had to be replaced.)
The microwave would not normally be on the GFCI circuit either (typically in the bathroom but controls outlets 'downstream' electrically - those by the kitchen sink and outside.) But no power to the GFCI is an issue.
Since you are taking it in for warranty work - add it to the list...