Other than on diesel trucks you will never solve a running problem on a Chrysler product by replacing the fuel filter. It sounds like the fuel pressure is bleeding down when the car sits a while. That is due to a leaking fuel injector, or less commonly a leaking check valve in the fuel pump, or much less commonly a leaking fuel pressure regulator. A quick way to verify if this is what's happening is to turn the ignition switch on, then wait a couple of seconds before cranking the engine. The fuel pump will run for one second to be sure the pressure is up and ready for starting. One second isn't enough time if the pressure bled down to 0 psi. In that case, turn the ignition switch on, wait for the fuel pump to turn off, (you should be able to hear its hum), turn the switch off, then turn it on a second time, then crank the engine. If the problem doesn't show up, it's a pressure issue. If you can live with that it won't cause any other problems.
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Monday, January 14th, 2013 AT 4:36 AM