I'm assuming the charger/converter once worked and that they did not leave the socket out completely. But you have a gang of Romex wires coming into the basement from your breaker panel. All of them leave toward their destinations within the rig. But there should be one that is dedicated to your basement and should be visible to you. The charger breaker in my panel only has one function and that is to run the charger. You should be able to locate that single wire close to where the bundle exits the panel on the rear basement wall then trace it to your charger. I think it might be a different color Romex than all the rest, perhaps Yellow or Orange. Like I said I found mine on a step up from the basement floor to the top of the deck that covers the water tanks. But I have also seen basement installs that were cleaner than mine also.
If all else fails, you can take of the cover to your breaker panel, then take out the breaker box altogether, and have someone move the charger wire back and forth while someone looks on in the basement for a moving wire. There should be sufficient slack in the wires behind the panel to do this.
Another idea is to take you cover panel off of your breaker box and see if you can see the insulation for the wire that connects the charger, if it orange, yellow or white, then you will know what you are looking for.
On the battery 11.5v is 10% state of charge, 7.6v is dead, so that battery has been completely cycled at least once and you were able to recover it to 14v some battery cannot come back from that, some good chargers can bring one back, its Ok. It probably will not fail from that one discharge. But you can get Autozone to check it for you, but before you have it checked leave it off your charger for 24 hours.