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If you only get water during rinse and not during the initial wash, you have a bad control board/timer (depending on if your model number uses a physical time knob that you twist to select the cycle, or a control board with buttons to select the cycle). Either way, the timer/board would need to be replaced to resolve this issue. It's the only part that can cause it to fill in one cycle but not another.
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OK then as I said before, that means you have a control board which would need to be replaced. You'll need the full model to look up the part and that is located on a sticker around the front frame of the tub and can be seen if you open the door.
That depends on the model number but usually it's about $150-200 for the part and if you're handy it takes about 20-30 minutes to replace.