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Your problem is the damper assembly in the refrigerator section, GE had to redesigned these because of your problem, we are starting to see a lot of these. This is what it says and how much it is.
Item #1055112 (OEM Part)
Refrigerator air inlet cover/damper kit with fan motor. Damper and fan assembly have been updated to prevent freezing in the refrigerator.
Manufacturer Number WR49X10091
you can order this at the following link, it comes with instructions also, http://www.repairclinic.com/PartDetail/Damper-and-Fan-Assembly/WR49X10091/1055112 this will take care of your issue in the refrigerator section, however you seem to have a lot more problems than that, have you heard any clicking coming from behind the refrigerator at all? You obviously have several different problems this one. It could be the motherboard