A scanner will not diagnose any battery or starter issues
Partially correct - if the batteries or the starter motor are the issue you are correct. However, cranking the engine involves several modules including the SCCM, TCM, PCM and the BCM and of course the HS CAN network.
Better advice would be to first check the charge and condition of the batteries. Second might be to remove the EZ LYNK and re-evaluate the no crank condition. Since the DLC device is not connecting with his phone, it either has no power or is defective/damaged.
The obvious question is what happens when the ignition is on - do the lights work, does the instrument panel come to life, HVAC, Radio etc. Starting system fault messages on the Message Center?