Since your microwave is powered by 120VAC, that tells you that side of the circuit is working. From there, the 120VAC goes into your converter and you get 12VDC out. The 12VDC powers all the systems you said aren't working. When this happens to me, I follow this procedure:
Disconnect shore power
1. Visibly inspect the battery connections to make sure that the cables are installed with the correct polarity. One some rigs, black is +12V, and white is ground.
2. Using a meter, check your battery for DC voltage. Hopefully, it's over 12VDC. If it is:
A. Check to make sure you don't have an in-line fuse that's blown
B. Check to see if you have a battery disconnect switch that is off.
3. If you still haven't found a problem, disconnect the battery terminals and make certain you're not plugged into shore power. Then, pull off the cover for the converter and slide the converter out of the housing. There are typically one or two fuses on the side or back of the converter that are in the 40amp range. Pull these fuses and check that they are good. If bad, replace them with new ones. If good, put them back in.
4. Being very careful to follow safe electricity practices, reconnect the battery, and plug into shore power and check for 12VDC (actually about 13.5VDC) output on your converter where the wires come out that go to the battery. If you have no DC voltage at this point, then your converter has likely failed and needs replacing.