I can't believe the amount of time I have wasted to discover this. I recently decided to upgrade one of my computers from the EVGA 1300 G2 Power Supply to the EVGA 1600 G2 Power Supple. I just swapped the supplies and the system booted right up. Then a couple weeks later I decided to put my old 1300 G2 into a new build, and it wouldn't boot.
Turns out the EVGA 1300 G2 and the EVGA 1600 G2 use different 24 PIN cables. The cables were even labeled as such with the 1300 G2's cable labeled as MB, and the 1600 G2's cable labeled as MB 1600W. Why on earth did EVGA feel it was needed to change the cables like this. To make it even more confusing the 1300 G2's cable works just fine on the 1600 G2, but not the other way around. All this time I thought I had a bad PSU, turns out it was the wrong cable. Let this be a lesson to everyone out there with similar issues.