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You have replaced the water valve in back so you are familiar with it . Remove the water line from the valve that goes to the ice maker ( it's the smaller diameter line and see if you can blow through it . If you can't this line is frozen and not letting water to the ice maker
Why wouldn't WHAT shut off ? Your question stated the icemaker wasn't working so what is not shutting off ? It is RANDOMLY making ice ??
I know you've replaced the ice maker but everything is pointing to it - not making ice , stalling occasionally while in fill. It is new , so take it back and try another ( it's under warranty )