If you accidently hooked the battery post backwards, or even just arced a spark while hooking up the battery, it may have blown a fuse either in the fuse block near the battery box, or the 2 fuses located in the back of your converter/charger. Follow your positive cable to the fuse block to check for a blown 12v circuit breaker or inline fuse.
Undo your battery cables and plug in to shore power to power up your 110 to 12v converter. With a volt meter check the positive and negative power at the battery cables. If the converter is working you should see between 13 to 14.5 volts.
Your refrigerator, and furnace have a circuit board that runs off of 12volts, therefore it wont work if no 12v is present, or if voltage is below about 10volts from the battery.