Vengeance RAM

I have a homebuilt with a Gigabyte GA-970A-D3 AM3+ MOBO, AMD FX-4100 CPU and 2x4=8 GB (1600) Vengeance RAM. I bought an additional 2 modules of the same RAM, with the only difference being the color (original is blue, new is black). My objective is to have 4x4=16 GB total RAM. When I install either of the black (new) RAM into a slot, the computer will turn on but not boot. This is in all configurations, with and without the blue (old) RAM. The black RAM works in an Intel platform (I purchased it used from a friend with an i5 setup), so I know the RAM is not bad. I realize the two sets of RAM are not paired, but the computer should still boot. Any thoughts?

You must ensure any CPU or RAM you install in any given motherboard is supported by that specific board by ensuring the CPU and RAM are listed on the motherboard's QVLs (qualified vendors lists). You must buy a listed CPU, but there are too many RAM makers and models for board makers to test them all, so you must buy RAM with the same specs as listed RAM.

Your board's QVLs are here.

Also, see Corsair - Mixing Vengeance Black and Blue RAM

i'd check the voltage of the black ram in the i5 system, might need 1.65v and your blue is 1,5v and what your motherboard supports.