Unless the compressor completely failed then you should be able to get it going again.
Look on the back of the refrigerator and locate a cover on the compressor.
This will be the relay.
Here's an image describing where the relay is.
Unplug the refrigerator and then take a screw driver and give the relay a tap.
Sometimes they stick and tapping it fixes it. If not you will have to get a new relay to put on it.
If that doesn't work then the compressor is probably gone in that case it would be cheaper to get a new refrigerator instead.