I was parked at my banks' ATM to deposit a check into my account. The car was parked and I put the gear shift in the Neutral position and applied the emergency hand brake. When I finished with the deposit, I released the hand brake. Then I moved the shift from Neutral to Drive and the vehicle did a sudden unexpected acceleration (the car left the parking spot like a bullet/missile). I attempted to apply brake pressure with both feet and there was no response. I caused a collision with parked cars opposite a chain link fence. Fortunately, the cars that I collided with were not occupied.