HVAC fan is on, but the compressor attempts but will not start

It could be one of several problems -

1) Failed compressor relay
2) Failed compressor
3) Failed component in the defrost system
4) Bad door gaskets
5) Failed door light switch

Questions to answer -

1) Is the compressor (large black domed item with three tubes (one stubbed) at the bottom back of the frig.) warm or hot? If cool, then you could have a failed relay inside the compressor enclosure. Unplug the refrigerator from the wall, locate where the wires go into the compressor terminal box. Remove the clip holding the cover, and pull the relay off the compressor. Inspect for evidence of burning. Replace if necessary and reinstall all covers. You should always hear a clicking sound when the compressor tries to start. If it does not start, and you hear it click again a few seconds later, then it's likely you have a failed compressor.

2) Was the condenser fan running? The condenser fan pushes rejected heat away from the condenser coil. If it's not running, it's hard on the compressor, and the refrigerator does not cool.

3) Was there thick ice buildup inside the louvers of the back wall of the freezer? Heavy ice buildup here is an indication of a failed defrost control or heater and requires further diagnosis to determine the problem. A knowledge of use of a volt-ohm meter is required, along with a willingness and ability to do some mechanical and electrical dis-assembly and test.

4) Was the fan running inside the freezer? Freezer fan should run when the compressor is running, but not during the defrost cycle (or it would slightly heat up the refrigerator.).

5) Look up my "Tips and Tricks" article on testing your door gaskets.

6) Open the door slightly and look inside as best you can. Is the light on or off? Continue to open the door until you see the light go on to confirm the light switch is working.

Following each of the above steps may not help you fix your unit, but will give you an indication of things to look for and describe when you post a request for help when trying top fix you refrigerator.