Product review (5 stars): As it turns out many like me have had the same problems and had great ...
I have a Magic Chef
50-Bottle Wine Cooler, Stainless Door
 Model No. MCWC45MCG
This unit stopped cooling approx. 6 years ago.
Living in the island of Maui parts or that of a repairman for these units are hard to come by.
With this being said I did a little research that would possibly help me figure out on what to do next.

YouTube of all places had enough to give me courage to attempt and challenge what is now working.
As it turns out many like me have had the same problems and had great success in getting their units back working.

Part I needed to replace:
P6R8MC-OR0506 = Refrigerator start relay. The start relay provides voltage to start the compressor.

Part I ended getting through Amazon
 LG Electronics part number 6748C-0004D
 Refrigerator start relay

Wine Cooler is up and running and very pleased with everything.