The pot is fine , i tested it on UNO, works perfectly. I connected the Pot terminals even at solder in the back of the board. NONE of the analog ports is working,but the DIGITAL are okay.
While the pot was connected(it was connected right) to the arduino , i used a meter to measure the voltage in the pot, while i changed the resistance value, but the output of the pot was at 5 v all the time...
Well you are going to have to figure out why you only measure +5vdc at the pot's wiper pin output wired to the analog input pin, even when you turn the knob through it's range. The fact that you only see +5vdc applied to the analog input pin needs to be fixed before you can expect the 2560 board to read the pots value.
Lefty