I have a OptiPlex 5040 with the motherboard listed as 0T7D40.  I could not find an official list anywhere though for what this board supports?  

It has a i5-6500 installed in it and I was looking to take that out and swap in a G3930 or G4560 that I have in a gaming pc.  The i5-6500 is faster and works better in my gaming pc, but I can't get either of these G Pentiums to boot. 

I'm on the latest bios I believe: 1.13.0 from 2/28/2019

This has the Q170 Chipset I believe which according to Intel supports all of these processors. Did Dell simply never add Kaby Lake support to their motherboard?  

The only difference I can seem to find is that the G3930 and G4560 are Kaby Lake CPU's and not Skylake like the i5-6500.