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If the compressor is humming till it makes a clicking noise then stops humming for a few minutes, if it keeps repeating this You either need a start relay or the compressor has gone bad if You post the model number I can locate a relay for You.
Look forward to hearing from You
Whirlpool makes Kitchenaid and around the time Your refrigerator was made they had a problem with the relays this kit will fix all models and comes with instructions to figure out which pieces to use and how to connect them
Let Me know how it goes
P.S. This was easy to spot if you remove the old relay from the side of the compressor and shake it, it will sound like it has a bunch of little pieces rattling around in it.
The sound You will hear is the PTC disc that failed.
Glad to hear the good news