I removed the back cardboard panel. Saw the fan running fine and couldn't hear any sounds from compressor (which was hot to the touch).
I unplugged the fridge and removed the starting device/capacitor from the compressor. Using a multimeter (and a few YouTube videos), I checked the compressor output. Then plugged the fridge back in and checked the output to the starting device/capacitor.
The compressor output was fine, the output to the capacitor was fine, but the output from the capacitor was bad.
I immediately ordered the parts needed (starting device and capacitor) then began to clean out the fridge. I luckily have a garage fridge that kept our food safe until the parts arrived. I also vacuumed all the dirt from the underside of the fridge and gave it a thorough cleaning.
Once the parts arrived, I put the new pieces in and plugged in the fridge. The compressor kicked on after a few seconds. I put the panel back on and placed an ice cube tray in the freezer. Once it was fully frozen, I felt comfortable putting all the food back in.