Hi and welcome to
FixYa. I am Kelly.
The humming noise your hearing is the evaporator fan blades striking the ice build up on the evaporator. The fact that you have ice build up is a sure sign your refrigerator is not defrosting.
The door switch controls power to the evaporator fan.
I am going to use this model number 106.57071791 as a parts reference that MAY be different from your actual model but it is close. This model is a mechanical control refrigerator. You may have the electronic control version.
Take a look at item 6 this link:
http://www.searspartsdirect.com/partsdirect/part-model/Kenmore-Parts/Refrigerator-Parts/Model-10657071791/0582/0165000/P8100197/00012?blt=06&prst=&shdMod=
It will be located in the top left of center & front of your fresh food compartment. It will be circular and will have 2 tabs on it with an incline so that if you were to rotate the tabs with something flat it would only turn ONE direction.
Either use your finger nail or something flat to SLOWLY rotate that until you hear an audible click. (Everyting stops but the lights) This is initiating an automatic defrost cycle. After about an hour come back and check to see if your refrigerator has re-started. If it has not restarted there is definately a problem with the automtic defrost circuit. That can be the timer (listed above), The defrost element under the evaporator, the Bi-metal thermostat on the evaporator or wiring.
All parts can be found via this link / section
http://www.searspartsdirect.com/partsdirect/part-model/Kenmore-Parts/Refrigerator-Parts/Model-10657071791/0582/0165000?pathTaken=
If none of the links work go to
http://www.searspartsdirect.com and enter your model number where it says find it fast and choose model search.
I guessed at the model number so if this does not resemble your refrigerator or you have the electonic control board type refrigerator please respond with your model number.
Thanks for choosing
FixYa,
Kelly