Outboards (2 cycle) are shut off by putting a ground on the power pack (OMC) or switch box (Merc). This is done using the black/yellow wire going to the switch. This same wire also goes to the emergency cut off and mercury switch that keeps you from starting it when the motor is tilted up. Find the black/yellow wire on your power pack and disconnect it. Put one lead of an ohm meter on the wire and the other on battery ground. With the key off you should read a direct ground and with it on an open circuit. Turn the key on/off several times and if it reads good every time then you have a bad power pack. If it doesn't read good everytime then either the ignition switch is bad or you have a bad connection going to it. If it points towards the switch/wiring look on back of the switch and you should find 2 terminals marked "M". One of them will have the black/yellow wire connected to it and the other have a black wire going to ground. Hope that makes sense.
Fair Winds and Following Seas
Bill H. PTC USN Ret
Chesapeake, Va