My wine cellar is not cooling down at all, the fan is running and it blows air in the inside also but never cools down

This is likely to be caused by the start/run capacitor on the fan. Call for service, you don't want your valuable wine collection mistreated!

https://www.google.com/search?q=Breezaire+Wine+Cellar+Cooling+Unit+service

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turn it on

try to defrost the unit check the evaporator fan if working good adjust the setting or lessen the setting of your thermostat maybe the thermostat cannot cut off after reaching the temperature setting then start your unit then observe.

How long have you had this unit and did it quit suddenly or did it fail intermittently. Do you mean running where you can hear the fan and the light comes on when you open the wine cellar door? If so, I would suspect the starting relay failure on your cooler which should be very easy to replace. There should be a wiring diragram on the back of your unit somewhere and could be labeled (RT). Your compressor would be the last thing I would suspect.

has the cellar ever worked right in your home? These small refrigeration units basically move heat from a conditioned space to another space that is not objectionable such as your home where your central air system then moves the btu's. This being said, the cellar has a ventilation system that must pull in room air and push out the box air. these vents must be clean and clear of obstrucions to ensure proper performance by the equipment

the evaporater fan should be opperating when the compressor is runnig ,as well as the condenser fan if you have one

Try tapping on the thermostat it is probably sticking.
If it comes on then you will need to replace the thermostat.
Check the start relay on the compressor.
Check the fan motor on the compressor is it running?
Clean lint from underneath on the condensing coil.

First question, do you have power to the unit and the cooling fan is not working? If this is the problem then sounds like one of the two fuses in back panel has burnt out.

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You'll need to replace the fan. The original fan bearings wear our after a couple of years. It's pretty simple to drill out the rivets and replace the fan. I suggest you replace all four with ball-bearing fan units.