I am no expert or anything, but had the same thing happen to me with my side by side. Did the same thing you described, cleaned under and behind, not seeing any ice anywhere. No help. Then,,,,,, I took the back panel off the inside of the freezer and the entire cavity was frozen solid. There are a couple places/ ports, where the cold from the freezer is transfered to the fridge side and they were froze shut. The wife and I defrosted it thinking that was all the problem was and put it back together. It helped for about 2 weeks then the same thing. Took it apart again, same thing. Turned out it was the defroster bulb was burnt out. Easy fix , about $30 in parts.
Hope this helps,
Randy
Randy Bell, October 2007