Which version of controller is this? The sticker in the battery compartment has the model number.
Check all 3 pins of that POT with a meter and see what they measure voltage wise. They each have a Ground, Wiper (center one) and Voltage (AN+) lead. Use one of the 4 big solder lugs for the reference (ground) for the meter and you should get 0v on one of the outside leads (ground) then 1.8v on the other outside lead. The center lead should be around 0.9v on a working POT, then vary from around 0v to around 1.8v when moved.
If you measure
#1 - 0v, 0v, 1.8v - There is a short between the Ground lead and the Wiper lead.
#2 - 0v, 1.8v, 1.8v - There is a short between the AN+ lead and the Wiper lead. Could also be an open on the Ground lead.
#3 - 0v, 0v, 0v - There is an open on the AN+ lead.
#1 and #3 will cause the same issue, Stick being pressed full Left.