I will be happy to help you out. The noise you are talking about sounds like the overload on the side of the compressor. You more than likely have one of two problems.
Either the relay on the side of the compressor is defective, or you have a bad compressor. The first thing you should do in a case like this is to replace the overload and relay on the side of the compressor.
If this gets the compressor running again, great. If not you have a bad compressor and that could be grounds for replacing the whole machine. But factors will affect that. Age, condition, and the machine may still be covered under a five year compressor warranty.
If you have anymore questions please feel free to ask. I will be more than happy to answer anymore questions you have about this.
Thanks for using JustAnswer.com!
I completely agree with you. I am a factory servicer and that's what I hear all day long. Usually an issue like this is common in a frigidaire made kenmore. Bad relays and compressors. Usually just over a year. Sometimes its just the relays and you get lucky. Or you may need to have the compressor replaced. Check your owner's manual to see what's covered and how long. Check the sealed system warranty.
If you have anymore questions please feel free to ask. Thanks Again for using JustAnswer.com!