Hi.
When the fridge is on put your hand on the compressor and check if you can fill vibration. If not then unplug it and remove the start relay/overload from the compressor and shake it. If it rattles - replace it
Part number: W10128791 
Before ordering a part using multimeter check the continuity between the compressor's pins and then to the ground. If the pins have continuity and no continuity to the ground then order the start devise.
Check the voltage at the outlet. The fridge wont work if there is less then 110VAC.
Here are the breakdown diagrams and
Unit parts for Whirlpool GX5SHDXVY00 - AppliancePartsPros.com
Simon.