Hi, Sammy. It 'sounds' like an ignition tumbler/switch issue. Probably just coincidental that it started after switching relays? When you mentioned that it would start when you wiggled the key, that is a classic symptom of tumbler/switch problem. With Chrysler products, I always replace both the key and tumbler along with the switch. A locksmith can change the tumblers in the new one to accept your O.E. key.
2008 Chrysler 300 v6 3.5L. Intermittently when I turn my key the car will not start. Sometimes it takes 4 seconds. Sometimes I have to jiggle the key to start the car. I thought I would check the starter relay first. In the fuse/relay box under the hood, I found 4 relays. I swapped the starter relay with the wiper relay because they are the same parts with same part number (Omron 21911C 05269988AA were the part numbers printed on those relays). By "swapping" I pull out the starter relay and in its socket, I plug in another relay that I unplugged from the relay socket that was for the wiper. I also plug the starter relay in the wiper relay socket. I found a Youtube clip that shows exactly this. https://www.youtube.com/watch?v=BIdy3HIwZis
After swapping the relays, the car starts fine and the wiper will not turn on. I swap everything back to how it was, and the wiper works and the car starting issue returned. I did this several times to confirm the bad starter relay. So, clearly, the starter relay was bad. So I ordered the relay online. However, the next day, I try swapping the relays again. But this time, car will not start even after I swap out the starter relay with the wiper relay. The car tries to crank few times but does not start when I use the starter relay or the wiper relay. The wiper works fine with the original wiper relay. The wiper will NOT work with the original starter relay.
I thought I tried starting the car too many times yesterday and drained the battery. I jumpered the battery. Still the same starting problem. The battery is 4 years old, so I went and bought a new battery. Still the same starting problem.
I am puzzled as to why swapping the relays works one day but not the next day. Did I burn out a fuse somewhere? Did I break the starter solenoid?