What is the position of the fingers on the icemaker that remove the ice cubes at in relation to a clock face? 1 2 3 4 O'Clock?
The ice maker itself is the problem, you should see the fingers at the 2 o'clock position, you can replace the icemaker with part number (NNN) NNN-NNNN, you can order it at http://www.apwagner.com/ or at http://www.repairclinic.com/, to order the parts, this will fix the ice maker problem you are having.
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Did the water problem to the door happen before this problem or at the same time?