Nothing to figure out. Dishonest mechanic.

There are 2 or 3 battery cables. Look under the hood and you will see where they go. One goes to the starter, one goes to the fuse box and one goes to ground. None of these would be affected by bad motor mounts. They are cheap and easy to replace. However there are many other cables in the car which would not be described as battery cables. Which cable is affected. Suggest you have this "mechanic" show and explain exactly what is wrong, give you a list of parts and prices and break down the labor charge. If I was considering spending those bucks I would want a second and third opinion. Please post back what you find out.

PS I will give you much more for the car and pay the towing to North Carolina.