Maytag stops cooling and makes a buzzing sound.

I recently bought this maytag that buzz’s every time the compressor starts. Sometimes it seems to fail to start the compressor and will continuously buzz. The previous owner said he replaced the relay but it didn’t seem to help so he bought a new refrigerator. Anyone got any ideas? I’m hoping I don’t have to replace the compressor.

You have a hard starting compressor, will fail to start during high power usage periods when the line voltage is low. An amprobe would confirm.
The use of a hard start kit on this modern compressor will lead to quick compressor failure and/or a fire!