I got this resolved... I talked with Scott at Eagle Machine in Houston, and he said to pull the main CPU board (Slot 5) and then pull the memory board off the main and replace it in Slot 5. Once I tried to power up the machine the noticeable "relay click" in the back cabinet showed back up! I walked around the machine to find that it started up properly! He thought it could be a faulty memory board.
In further troubleshooting I reinstalled the memory board on the main and it fired right up again. So not really sure why it was messing up, but this will be the first thing I try in troubleshooting my machine.