Hello and welcome to JustAnswer.
I am thinking that you have a problem with the TIPM (Totally Integrated Power Module). The TIPM is the fuse/relay box located under the hood at the right front corner of the engine compartment. I see a lot of TIPM's fail and cause this type of problem you are having. This needs to be checked using a capable scan tool like the dealer's StarScan tool, or one of the newer SnapOn scan tools. I am afraid that you will need to get the vehicle to the dealer, or an independent shop that has a capable scan tool to check this out for you. Without these tools, it will be difficult to properly diagnose.
I hope this information helps, and let me know if you need further assistance with this.
I understand what you are saying, and I see that your vehicle actually has a separate FCM mounted to the IPM (which is the same as a TIPM) and still needs to be diagnosed with a scan tool. It will probably need to be replaced. You do not need to go to the dealer if you can find a reputable auto electric shop that has the appropriate scan tool. Here is a description of the IPM/FCM from the factory service manual so you can see for yourself.
08 - Electrical/8E - Electronic Control Modules/MODULE, Front Control/Description
DESCRIPTIONThe Front Control Module (FCM) is a micro controller based module located in the right front corner of the engine compartment. The front control module mates to the power distribution center to form the Integrated Power Module (IPM). The IPM connects directly to the battery and provides the primary means of circuit protection and power distribution for all vehicle electrical systems. The FCM controls power to some of these vehicle systems electrical and electromechanical loads based on inputs received from hard wired switch inputs and data received on the CAN bus circuit.
My 2006 Chrysler 300C 5.7 liter didn't need anything more than a new battery. Even though I tried to jump start the vehicle by hooking up jumper cables to my truck & got very little response, I completely disconnected the vented battery in the trunk from my car & removed the battery from my truck and connected to my car. My car started up right away; so, I bought a new vented battery for $153.00 and resolved my problem.