Back of Fridge icing up

Ok. UNPLUG the refrigeator. Take the shelves out of the freezer. Remove the back cover panel. If the coil is iced up. you can use a hair drier to though ice out. Be careful not to leave hair drier in one place to long the heat could warp the plastic in your liner move it around. Next when the coil is all clear look at the top of the coil there is a little 2 wire component that is straped to the coil. This is the thermination stat. when the coil is cold the bimetalic switch is closed this allows the heater to energise and defrost the coil. It opens when the temp at that spot reaches a set temp. turning off the heater. Then the defrost timer on the board finishes timing out and brings the compressor back on to start another cycle. unclip it from the coil look at it and make sure it's sealed around the top. you can sometimes submerg it in ice water and you will hear it click. if it looks good and it clicks its more than likely good.
At the bottom of the coil is usually a little metal plate secured by 2 screws. Behind this plate is a glass heater tube. there is a wire into each side connected by a spade terminal. look at the heater see if you can see if it is broke inside sometimes the glass is black looking and hard to see through. If it falls apart in you hands it's bad.
If both these components are ok. Then your problem is in the electronic board mounted under a meatl plate on the back of the refrigerator. I usually order the boards online from the manufacture. They usually run $185.00 or so. Hopefully your problem is the termination stat or the heater. If you find one component bad replace both. The other could have been damaged in the failure. Hope this helps