Q: Accelerator is not responding

Your key battery should not have anything to do with the way the car runs once it is started. The problem you are experiencing when pressing the accelerator may be related to many different things, but could be related to things like low fuel pressure, dirty fuel injectors or potentially a faulty throttle position sensor. The throttle position sensor (TPS) is a sensor used to monitor the throttle position of the throttle plate inside the throttle body in relation to your foot position on the gas pedal. Based upon the inputs from the sensor reading your foot’s position on the pedal, the ECU then makes the direction to supply more or less fuel to the motor. When this sensor is not working properly, this can cause intermittent responses when pressing the gas pedal. I would suggest having a professional from Your Mechanic come to you home to diagnose your throttle control system.