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Unfortunately this is not an easy issue to fix on these bottom freezer top refrigerators. You will want to unplug the unit for 24 hours to allow all the ice to thaw out. Once the ice is thawed out, the best way to clean the drain line is from the bottom up because going at it from the inside is really difficult. If you pull the refrigerator forward and remove the bottom access panel and locate the rubber hose which comes down directly from the middle or so of the freezer floor toward the back and use something like a turkey baster to shoot hot water up the hose. Once it's clear and you can blow air through the hose, you're good to go again. Also, if you have the ability to just unplug the refrigerator for 24 hours that'll thaw all the ice out and them you can just blow air up and clear the drain out.Now this drain hose has been re-designed because the material on the hose would break down and the check valve inside won't allow water to flow out so below is a link to the new re-designed hose you'll want to order and replace with instructions.
CLICK HERE for drain hose
Your electronic water valve isn't working properly or you have poor water pressure to the refrigerator from your house. You need to make sure the refrigerator is getting good water pressure and if so then you need a new electronic water valve. That would cause the slow trickling and it needs to be replaced. Below is a link to the valve you'd need to order and replace for your model. The water line going to the icemaker is likely frozen at this point since it had such bad water pressure getting to the icemaker so unplugging the refrigerator is probably the best option to fix both the drain and this new issue.
CLICK HERE for valve
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