Thank you for all the suggestions. Right now I will work on testing the things that have been suggested so far. The power management monitor is reading E0, 123V, 0A 60H. Also the microwave does not have power. I will work on getting a new dogbone connector and sperry tester as suggested by John.
I also verified everything again that I mentioned in my earlier postings since these things seem most like to occur late at night :-). Ollie plugged in and the inverter powered off on the inverter box itself (the power button on the inverter display doesn't seem to do anything). There is no power to the outlets. As soon as I turn the inverter on they power up, but I am trying to keep it off so as not to run the batteries down anymore. Another hour or to till the sun comes up!