Can you boot into button test code? It might tell us if there is a bad connection to one of the buttons internally.
Button and LED Test Mode After you have completed the factory lock/unlock programming, you may put the controller into a special LED and button test mode. To do so, begin with the controller powered off, then hold Left Bumper + Right Bumper + Back Button while powering up the controller. (Be sure to continue holding that three button combination for several seconds after the controller powers up). The controller will play back all the available colors on the LED indicator and then perform a button test. During the button test, the LED’s will blink a certain number of times to correspond with each button press. Here are a list of button presses below, but note that if you let go of all the buttons, nothing should be flashing. If you let go of all buttons but it's still flashing, count the number of flashes and report back here:
Button Number of LED Blinks when pressed
D-Pad Up 1 quick blink
Right Stick Center 1 regular blink
D-Pad Left 2 Left Stick Center 3
D-Pad Down 4
Button Y 5
Left Bumper 6
D-Pad Right 7
Right Bumper 8
Button X 9
Sync Button 10
Back Button 11
Button A 12
Button B 13
Right Trigger 14
Left Trigger 15
Mod switch on PAD1 16
Tac switch on PAD2 17
Tac switch on PAD3 18
Tac switch on PAD4 19
Tac switch on PAD5 20