Dandy. If you have the Chrysler transmission, the neutral safety switch was connected to one of the smaller studs on the solenoid. In the other version that stud gets 12 volts switched onto it only during cranking to bypass the ignition resistor. If the second version is used in place of the first one it shouldn't even crank, but if you bypassed the solenoid to get the engine started, it would stay running with the ignition switch off because current would go through the solenoid's coil to the ignition system and keep it powered up.
If this failure to stop just started acting up without any replacing any parts, I would have to guess that switched contact is sticking in the solenoid. I've never heard of that happening but that is the logical conclusion. Pull that small wire off the solenoid. If the engine stops, that contact is sticking.
Wednesday, May 1st, 2013 AT 4:35 PM