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When this occurs are you opening and closing the lid and then advancing it to the spin? Have you tried just turning the dial to spin without touching the lid at all? This is important because if it is the lid switch when you lift up the lid to check to see if there's water in it you are resetting the switch and then when you put this in spin it will spin. Try running a load and see if it goes all the way through to the end without spinning. Then
I'm pretty sure the washer spins when advancing to the spin cycle without opening the lid, but I am not running a load at this time. Also, my wife tells me that the cycle worked when she occasionally lifted the lid to check on it.