the wire that sends the signal to the started and the wire that tells the engine to shut off are different, ignition switch could be the problem. it may be telling the motor that the key is off. im not sure if that circuit is supposed to be open or closed, but should be able to tell by probing the wires going to key switch and seeing wich one changes between key on and key off. check by the switch itself and again near the motor. if niether changes its your switch, if it just changes at the switch then its the wire. you see in the movies when they hotwire a car, they always twist the two wires together, thats to "turn the key on" then they spark the other wire to the power to send the signal to engage the starter.