Check your voltage on the battery. Should be 13.8 on the dash, and likely functional at lower levels.
Shifter could be the problem.
There is a stalk inside the shifter stem that must be pulled UP to change a gear. The thumb button does this. If the thumb button on the shifter has lost its 'linkage', it is not going anywhere. Does the button feel correct? If you feel so inclined, you can easily remove the shifter handle and pull the stalk manually by popping the trim and unclipping the handle (big metal 'staple'). Doing so however means you'll need the dealer to reinstall the handle (cost me $50) unless you have the button setting tool.
The rest of the shifter mechanism looked fairly rugged, but tight. I doubt something could have wedged inside that mechanism with the shifter cover intact. The shifter cover (the black slide) can get jammed if an object gets caught. See DIY Shifter article in DIY section on this.