Why is my compressor not running

There are multiple reasons this could be happening. Since you haven't posted the model number, I'll just list a fair few. The compressor could have a broken winding internally. To test, unplug the fridge, disconnect the wires to the compressor, and do reading across the windings. Go from start to common, make a note. Then check from run to common. Make a note. Then from start to run. S to C and R to C should add up to equal in the area of the ohm reading of R to S. It won't be exact but it'll be in the ball park. If any of them read OL then it is toast. Could also be start components. Is the starter relay engaging? Is the capacitor good? Are you even getting power to the compressor/starting components? If not, then look above. Could be a control board depending on the unit, or a tstat. Or it is stuck in defrost. Move the thermostat setting up and down. Go lower than you normally set it. I have seen thermostats drift. Did it kick on? When you reply please post the model number so we can see what it actually has, please. The more info the better. Without it we can throw suggestions all day without even knowing if it has all the components we mention.