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Generally the parts that fail in the defrost system are the defrost heater (check for continuity), the defrost timer (put it into defrost manually and watch to see if it will turn off) and the defrost thermostat (check for continuity).
To troubleshoot this you will need a basic tools and a multi-meter to check ohms and maybe voltage.
Please post the model number so that we can give you more specifics and see what you are looking at. It will be on the inside wall of the fresh food compartment.
Let me know if you need any more information.