I just bought my first camper. It's a 1990 Cascade 8 1/2ft. Plugged into 110V everything (fridge, lights, furnace) works great. When I use the 12V battery everything except the furnace works. It's a brand new and fully charged battery.
Any ideas why?

Are you sure the fridge has a 12 volt motor? What lights the burner? Pilot light? Spark Ignition? Hot Surface Igniter? If one of the last two, could be that that component is not operating on 12 volts. My best guess is the 12 volt igniter is bad. Put a meter on it and see if there is continuity. Yes means it is OK.

Thanks mh45472

At the risk of sounding like an idiot I think the fridge has the spark igniter system (I turn on the gas and hit the striker button a few times until it lights).
If you were meaning the furnace, does it actually have two separate igniters, one 110 and the other 12V? Also noticed it has a CO detector that comes on when 110V is attached but not when the battery power is used.
I am using a Marine deep-cycle with 660A battery. Anything wrong with this?

My fridge operates the same way. The striker is actually lighting a small pilot light when operating on gas. In addition, my fridge has a 110 volt igniter to use when on AC and a 12 volt igniter for use when on DC (battery). I suspect your furnace may be set up similar and your 12 volt igniter is not working. The CO detector may work once the furnace ignites using DC. There is a sequence to the ignition process. Your battery should be fine.

Many thanks mh45472

I'll look into the igniter thing. I forgot to mention that it is on a thermostat system as well but I'm guessing that doesn't make a difference since it works fine on 110V.