I had this problem a few months back where the car would start and run fine but when I would go to shut it off, it would stay running as if the key was in the on position. I could turn the key off and take the key all the way out and it made no difference. The car has a new starter solenoid in it and i have not altered any of the wiring. When it did this over the summer, I put a spare ignition switch that I had sitting in my garage into it and the problem came back a few days later. The coil in the car went bad also and actually looked as if someone had put a firecracker in it. The car wouldn't run at all. I replaced the coil with a brand new one about 4 months ago and have put about 700 miles on it with everything working great. The new coil seemed to fix the problem. About two weeks ago, I went to go get lunch and pulled into the parking lot and went to shut her off and guess what? she just kept on running. Does anyone know what to check before I start throwing parts at it? BTW: the ignition switch that I put in the car was far from new. My dad had it sitting in a drawer and doesn't remember how long he's had it or where he got it so it's possible that it could be bad also.

68 Coupe 302 4bbl auto.
Edelbrock alum. intake and 600 CFM carb.

 

Starter Solenoid - again. I had one brand new out of the box from NAPA that was bad on install. I took it back and got another one, but I opted for the more expensive one the second go around. The first one was $14 part, the 2nd one was $21. So far so good...the only difference in the two was the more expensive one weighed more

Have you done any rewiring to the ignition/coil system? Such as adding an MSD unit....

 

Pull the wire off of the "I" terminal of the starter relay. If the car dies, the relay is stuck, replace it (as Wayne stated above). If that doesn't help, you are going to need a test light and a diagram to find your "extra" coil voltage source .

 

It just did it again today and I remembered the suggestion to pull the wire off of the "I" terminal on the solenoid and the car shut right off. I guess that means this is the problem? Come to think of it, When I put the new engine in, I put a new solenoid in (the old one worked fine, just looked old compared to the rest of the newly painted engine bay) and I never had the problem before that.
I haven't changed or added anything to the electrical system at all.
Thanks for the advice.

 

going from past experiences, it could be a bad solenoid that is malfunctioning or it could also be a combination of the solenoid and the points in the coil could be going bad or dirty.

 

I had this problem on my F100. If you pulled the "I" wire it would cut off. The solenoid wasn't my problem at that time. The stator in the alternator was bad and sometimes the diode bank would back feed through the solenoid to keep the ignition powered.

I am not saying the solenoid could'nt be the problem, just that if that doesn't fix it have the alternator checked.

 

Make sure the solenoid is securely connected to the fender apron.