So, it turns over but does not start?
Fuel pump?
This was going to be my next question.
Otherwise, there are three parts to any electrical circuit. 1) the power source. 2) the path. 3) the end user. You've effectively replaced the power source (the battery), and you've confirmed that it turns over when jumping, so that rules out the end user (the starter), so if it lies in the cranking system, it's somewhere in the path, I.E., the wiring and connections.
If it's cranking but not firing, then is the fuel pump not pumping? Is the ignition feed getting it's signal through the BCM? There was a fuel pump relay recall, but I don't think it covered 3.6's.
Also, removing the battery shouldn't reset anything. I've had mine out many times without issue (other than the clock issue).
One off the wall question, obviously you've driven it, which means it's started and run at some point, but have you put the key fob into the center console nook and let it resynch (best term I can use here) to the car? These push button start cars rely on a security rolling code to be run using the key fob as the pass through for authentication. If it's not synched properly... I know over winter, I have to go over to where I have it stored every month/month and a half and just cycle the locks to re-communicate the fob to the car as it goes in to to a sleep/dormant mode. I did this last week as a matter of fact. And this car having sat...