Replaced the inverter. Fans were still running, and the motherboard was putting out correct voltage to the inverter. When I removed and inspected the inverter I saw that it had a brown, silver dollar size burn mark on the plastic housing indicating it had overheated and something inside had blown. Because of that it was not sending out the correct voltage to start the compressor (I had already checked for correct ohms on the compressor and it was good).
Always check for the obvious first. Look at the front and back of the motherboard (main control board). Does it show obvious signs of failure like black or brown burn marks on the circuit board? Same with the inverter.
Below I marked that the repair took 2+ hours, but most of that time was spent diagnosing the various electronic components with a multi-meter. I had never attempted an appliance repair of this magnitude so it took me awhile to figure it out. If I had to do it again, it would take me half the time. A cheap multi-meter can be had for less than 20 bucks and there are plenty of videos on YouTube showing how to use one. Don't be afraid, you can do it! Also I must say that AppliancePartsPros low prices and liberal return policy was a big deciding factor on whether or not I did this myself, so kudos to them!