Wow! You are seeing voltage on both sides of breakers/fuses, but only microwave is working...strange. Also nothing to the 110V outlets? I had a similar problem and it was the battery kill switch was only partially engaged. I would suggest unplugging power from house, disconnect battery, then go through and open all breakers, then close them, maybe even pull all fuses, then reset them, cycle the kill switch to the battery, then hook up "Fully Chagred" battery, then finally plug in 110V power and see if it persists. Beyond that don't know, good luck and please let us know how this shakes out.
2006 Nissan Xterra
B&M Trans Cooler
2011 Nomad 206
Panasonic/Pioneer/Kicker ~ Audio/Video System
Days Camped /2009 / 33