Will your DC appliances work without using the shore power cord, using only your battery source?

Is the battery charged and the master switch on? What is your voltage at the battery? Have you checked the battery's terminals for corrosion? When was it last charged and how old is it? When was the electrolyte levels last checked? Lots of questions all concerning the battery's condition.

Your shore power should charge your battery and provide 12V DC to your LQ. If you have no DC from any source, then I would check your fuses again. There are a different set for your DC power than your AC power.

Gard

I keep the trailer plugged in all the time.   When we checked the batteries last night, they were completely dead.  We charged and reinstalled them last night.  Now, this morning, they're almost dead again. 

The batteries are in good condition - they have water and are accepting the charge. 

You may have one of two problems: older batteries or something on a circuit that is draining your batteries. Depending on the age of your batteries, they may not be able to hold a charge any longer. With some brands you're fortunate to get three years out of a set.

Do you have a battery master switch? If it is turned off, will the batteries still be depleted overnight? You may have an appliance or an electrical device that is causing a draw on your batteries. With the switch off, this should not happen. With a VOM, you can test for any current flow from your battery with the switch off.

Another way to test your batteries condition if you don't have a meter or light bulb, would be to again charge them. Remove the B+ cable and let them sit overnight. The next morning, reattach the cable and see if your appliances work. If they do, you have a device that is draining them.

Gard