Q: Car shakes while in idle and doesn't want to accelerate

The spark plugs are wet from trying to start the vehicle which is a good sign because this means that the motor is getting fuel. When the motor struggles to idle, this is generally a result of things like low fuel pressure or a dirty or faulty idle air control valve. The idle air control valve reads the air intake as it is mixed with fuel prior to being injected into the engine at low speeds and at idle. As this valve is controlled by the vehicle’s computer, it will adjust idle speed based upon other measurements such as engine temperature, intake air temperature and electrical system load or voltage. When you accelerate, the engine RPM increases, and as you let off the gas, the RPM slowly returns to the normal idling speed. When the engine RPM drops below the normal range of 750-800 RPM (for most cars), this often times will cause the engine to stall indicating a dirty or faulty idle air control valve. There is a brief transition period between idle and acceleration in which the idle air control valve no longer functions as it’s purpose is to regulate idle speeds and deceleration. The struggle to accelerate may suggest other fuel delivery issues such as dirty or faulty fuel injectors. I would recommend having an expert from YourMechanic come to your location to diagnose and repair your idle air control valve.