Grace's Neon Doesn't Know When to Quit

Dear Car Talk | May 02, 2013
Dear Tom and Ray:
I have a 2001 Dodge Neon with more than 150,000 miles on it. Until very recently, it's been an extremely reliable vehicle, and I've loved it. Lately, and at random times, however, the engine will not shut off -- even with the key removed from the ignition and in my hand! I've already gotten a new key and replaced the entire ignition cylinder, but it happened again yesterday evening.
Luckily, yesterday I was able to fiddle with the key a little bit and finally get the stupid thing to shut off. What could be causing this? At this point, the mechanics I've taken it to haven't been able to identify or fix the problem, and I can't find anything on the Internet. Each time it's happened, my local mechanic has disconnected the battery, which made the car turn off. After that, though, it runs perfectly for maybe a couple of months, until it happens again. Any idea what could be wrong?
-- Grace
TOM: You're a lucky woman, Grace -- you can't get your Neon to stop. Most of our customers with Neons can't get them to start!
RAY: You say you replaced the ignition cylinder. But that's just the locking mechanism that the key fits into; it's not the ignition switch itself. So you easily could have a bad ignition switch.
TOM: But before you replace the switch, try replacing the ignition relay. Rather than have a huge amount of current running through the steering column to the ignition switch at your fingers, the ignition switch signals a power relay under the hood. It's that relay that actually sends current to the engine's computer, which enables the engine to run. That relay could be faulty and sticking in the "on" position.
RAY: The relay probably costs 20 bucks, and it takes two minutes to replace. So start there, and see if that fixes your problem.
TOM: If not, then it's almost certainly the ignition switch, because there's really not much else that could cause this. But since replacing the ignition switch will cost you several hundred dollars, don't do that until you've ruled out the $20 fix. Good luck, Grace.