What part of PA are you from? I'm in Phoenixville and could probably work on your game. But as Levi said, $200 just about gets a tech to the door these days. You might figure on more like $400-700 as a WAG, depending on how much is wrong. And that doesn't "shop" your game or add any mods. Or fix the left side fading. Just gets it working.
The big unknown is the dead batteries, which in my experience means there is a 50-50 chance that the MPU is damaged. Possibly in need of complete replacement. But if you're lucky, it will just need a new battery holder soldered in. Send close up pics of the battery holder and components just below it for a better idea.
The coil could be wiring, a coil, a transistor on the board, or any number of other things. It will take some time and money to straighten it out. Not thousands, but hundreds for sure. But, all said, you got a screaming deal and should be happy whether you fix and keep it or sell it as is!