While you've received lots of good advice about the fridge controls, little has been said about your dead battery, part of your initial post. Completely discharging a battery isn't good for its health, especially if it sat for a while when fully discharged. I'd go to an auto parts store and get a specific gravity battery tester. Draw fluid from each cell in turn and check it for little black particles in it. (Return the fluid to the cell after examining it.) If you see them, replace the battery. If you don't see them, you still may have killed a portion of the battery's capacity.
An automotive load tester does not usually provide information about the health of a deep cycle battery. When the batteries in my 2011 Georgetown failed, they easily passed the load test used to check the health of a car's starting battery but when I ran a deep cycle test on them, they were only good for around 40% of their rated capacity.
Phil
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