When a refrigerator suddenly stops cooling there can be several causes.
The on/off thermostat might have failed. Try turning it off and then on. Give it a tap or two to see if it might start up.
The refrigerator might have stuck in the defrost cycle. If the defrost timer fails in defrost then the refrigerator will not run.
If you hear a hum and then a click it is likely the compressor or relay is at fault.
I would suggest you start with the thermostat and the defrost timer. The image below will help you locate the thermostat and defrost timer.
The thermostat can be checked for continuity when turned on if you have a meter. The defrost timer has a circled piece in the middle keyed for a straight screwdriver. It can be turned clockwise with a screwdriver or even turned by a quarter. If you turn it and the refrigerator starts to run then replace the defrost timer.
I hope this has been helpful to you.
You can reply with any additional details for further assistance.