All the user-accessible parts of the power center are behind the flip-down door of that brown box... the main AC breaker, AC branch circuit breakers and the 12VDC fuses (the multicolored plastic rectangles). The converter - the part that charges the battery - is integrated into (behind and underneath) the breaker/fuse area and has its own breaker to enable the AC to DC (battery charging function).
The microwave has nothing to do with the 12V side of the system (converter or battery), it runs strictly on AC. Its possible the breaker for it was tripped at some time. With most tripped breakers you need to move the handle fully to the OFF position before they can be reset to the ON position.
It happens fairly frequently that the battery gets hooked up backwards if it has been removed because, unlike a car, on a trailer the black cable goes to the +ve and the white goes to -ve (this follows the residential 'white is neutral' scheme). When this happens, the two 40A fuses (the brown ones on their own) will blow to protect that side of the system but everything AC should still work. They are awfully difficult to find in stores.
2015 Rockwood Signature UltraLite 8282WS Platinum, GY Marathon LRD, TST 507RV TPMS
2005 GMC 2500HD CCSB D/A, Curt E16, Prodigy P2, Garmin RV760LMT w/BC-20 b/u cam