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So when you go to start the Jeep you turn the key on wait a little while and the check engine light comes on and you may or may not hear a click and a hum and then the jeep will start and run, this most likely is worse when the Jeep is cold and a little better after it has been run and not allowed to cool down fully
We have seen about a couple of dozen of these over the years in the shop, it is always the early built (ZJ) Grand Cherokee 1993, what is happening is that the power converter inside the engine control module is starting to fail not allowing the controller to fully wake up until it builds a small amount of heat up inside the converter which is inside of the engine controller, The only repair that we have found to be effective is to replace the engine controller with a new Jeep part, when you get a remanufactured from the part store it may still do the same thing as the converter passes the bench test when they rebuild it, after having had this problem a couple of times we will now only use the new Jeep part, this controller is very costly, the last one we changed had a list price of $885.00, we have a few people that have not fixed this and waited for full failure which is impossible to tell you how long that will be, it could fully fail tomorrow or not for a long time
I hope that this helps you
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