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The fact that you unplug the unit and it starts to work again means that the problem is definitely one of the control boards. Now the display board wouldn't cause this issue, but either of the 2 main control boards on the back of the refrigerator behind the access panel could cause this problem. Most likely the issue is the main control board but since you can't test to be 100% certain, it's always a bit of a gamble. The part number I would replace is part number W10120827 which is your main control board.
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