You will never solve a running problem on a Chrysler product, other than the diesel trucks, by replacing a fuel filter, plus, if it runs with a push start, obviously the filter is ok.
When it doesn't start, do you hear a single, kind of loud clunk from the starter each time you turn the ignition switch to "crank"? If you do, suspect worn contacts in the starter solenoid. They can be replaced for 20 bucks but most people just replace the entire starter. If this is the cause, it will start eventually if you cycle the ignition switch to "crank" enough times, but the problem will get progressively worse over the next weeks and months as those contacts continue to wear.