Sounds like a similar problem that we are having on our '14 Titanium, except ours stopped starting with a whopping 38 miles on the odometer - the day we brought it home. Keyless. Pulled into the driveway and the next time I tried to start it a big nothing. No crank, no click. The displays went through the whole process as if the car had started though - could take it out of park, indicators lit up, auto headlights turned on. Press the start/stop button and it went through all the shutdown motions - dashboard deactivated and shift lever locked, lights turned off. Same thing if I used the remote start. Did everything it was supposed to do except actually run.
If I put the car into ACC mode (press start with foot off of brake), it threw a ton of fault codes one after the other. Got on the phone to the dealer, had to contact road service, two hours later a tow arrived and took our new car away. Dealer checked it and says it needs a new computer (PCM?) and they were ordering one. That was a week and a half ago. Do they strap these parts on the back of a turtle for delivery? Needless to say we are unhappy, both with the immediate failure of our $30K+ vehicle and the nonchalant manner in which the problem is being addressed. Shame that the part couldn't have been shipped out half as fast as they cashed our payment check.