A system for controlling starting and stopping of an engine that prevents a user from erroneously determining that the system is not functioning properly. The system includes an electronic key that may be inserted in a socket. The key selectively transmits a key ID code and a key transponder code to the vehicle. A microcomputer installed in the vehicle checks whether the key ID code matches a vehicle ID code when the key is arranged in the vehicle and checks whether the key transponder code matches a vehicle transponder code when the key is inserted in the socket. The microcomputer enables the starting of the engine and selectively interlocks the key inserted in the socket in accordance with the checking results. First and second display lamps notify the user whether the key is removable from the socket in accordance with the operation of the microcomputer.