Perhaps try contacting EA here:
http://help.ea.com/en/contact-us/new/
Or perhaps Xbox support:
http://support.xbox.com/en-US/contact-us
The 360 controller analog sticks have potentiometers on them.. but this is usually to fix "drift" or a neutral position off. Weird.
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Perhaps you could try fully uninstalling the game and trying again if you are 100% sure the controller is fully working.
