Yeah that battery has been pretty deeply discharged at 11.6v. It'll take a some charging to get it back.... if it going to come back.
When you measure the votlage on the system the 13.8 to 14.2 optimum spec is at fast idle, AND with the battery fully charged. It does not sounds like you are measuring voltage at fast idle, and the battery is certainly not fully charged. Measuring voltages in those circumstances can mean a lot of different things and so no one can say what you really have for sure.
Put the battery on the charger for a full 12 hours.... no shortcuts. Then take it off for an hour and then measure the voltage. Then start and run the engine at fast idle for a few minutes, and then check the voltage across the battery with the engine still at fast idle.
Taking readings in this fashion is the only way anyone can get a good grip on what is going on; running the tests right is needed to get past educated guessing.
