Refrig problem

Ok, first, keep in mind that I've had this a few years and everything has worked properly before. That being said, here's the problem: I have one of the Dometic 4 door refrigerators. The other day while getting ready for a trip I screwed up and hadn't had the solar panel plugged in to keep the battery charged while in storage, so I managed to draw the battery down below usable levels with the 12 volt stabilizers and the 12 volt jack. When I turned the refrigerator on to get it cold it got down to the 34 degrees I have it set at but in re-hooking it up the next day as I said, I managed to draw the battery down so much even the L.E.D. interior lights BARELY lit up and so the refrig quit cooling, showing code E4 which is DC voltage out of range. Plugged in a battery charger even though I had the 7 pin plugged in (even though the 7 pin was plugged in for some reason it wasn't pulling from the vehicle batteries) and the fridge even threw a E3 code which is cooling unit has malfunctioned. Well, once I got the battery charged up enough the fridge quit throwing codes and started cooling again. However, after a few days hooked up at my destination on 110 (even trying it on gas instead of just electric) and having it stay at 34 mostly, while traveling back home after seven hours it was up to 44 degrees. Note; I did have the battery checked to make sure it was OK and was told it was good. Anybody got any thoughts? As I mentioned before, I've had it a few years and have never had the temps go high like that while traveling. Thanks for any help you might have.