If your battery is dead and the converter isn't supplying a charge, nothing will work. Your RV needs 12VDC to run practically everything including the fridge, AC, furnace, and lights. You found out the microwave doesn't require 12VDC. If you plug your truck in and everything works, that, to me, points the finger at the converter. Your battery isn't getting charged. You could put at external charger on your battery to see if everything works and if it'll take a charge.
2015 Greyhawk 29MV
Honda CRV toad with Blue Ox baseplate
Ready Brute Elite towbar with braking system
TST 507 Flowthru TPMS