The engine stutters and shakes the whole car when I accelerate too quickly. The engine light comes on and the car loses power and speed, and shakes violently until I turn it off. Upon turning it on, the check engine light is still on. I found out that the light will go off and the car will run properly when the battery is disconnected.
Does anybody know what the problem might be?

 

Does the issue start again when you accelerate? It sounds like your engine is missing due to spark issues. Change your plugs recently, if so you could have a bad wire. Can you hook up to ODBII to read the code.