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You may be right on this. However, it may be caused by other issues, not only the defrost system.
It may be:
* Defrost timer broken
* Freezer fan broken
* Air entering into the freezer.
* A leak in the sealed system.
As only a technician can determine the exact source of the problem, it's a good idea to find how much is a new fridge and how much the repairs will cost.
Good luck.