Never ran into this where the odometer was still working. I suspect there is a broken connection on the back of the instrument cluster, but first I'd find a mechanic with Chrysler's DRB3 scanner and run the tests. A lot of independent shops bought them because with an additional plug-in card, they will do emissions-related stuff on any brand of vehicle starting with '96 models.
One test will run all the gauges up in steps, then back down. Another test looks at the Body Computer, (Central Timer Module) to see if it is reading vehicle speed and passing that information to the instrument cluster. You can also check for diagnostic fault codes in that computer.
The fault codes will stay in memory even when everything is working, but functional tests have to be done while the problem is acting up. Once it is verified it's not working during the gauge test, tap lightly on the cluster. If that gets it working, suspect a bad connection. If carefully wiggling the ignition switch solves it, we have to discuss inspecting the terminals in its connector. I suspect wiggling the switch didn't solve anything. I think it was just the vibration that got the speedometer going.
Unlike cars and trucks from years ago, there are not individual wires going to the instrument cluster for each gauge. Information travels between all the computers on two wires called the "data buss". When the other gauges are working, we know the data buss and those connections are okay. Basically that leaves the connections on the speedometer itself. Of course there's a pile of other computer circuitry in there, but that is rarely affected by vibration.
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Tuesday, October 14th, 2014 AT 9:51 PM