None of the Analog Read Examples are working with 2560

Well the picture doesn't tell us if you correctly identified the pot's wiper terminal to wire to the analog input pin. You should take a multimeter voltage reading from ground to the input pin to see if the voltage does change from 0 to +5vdc as you move the pot's know through its range. Also 110K ohm pot is awful large value, analog input pins work best with 10k ohm or less of source impedance.

Lefty