Greetings,
I may be missing something but here are my thoughts on this problem.
You have four memory slots. Two slots are blue (slots 1 and 2), two slots are black (slots 3 and 4).
The PC supports dual channel and single channel memory.
The slots are color coded for a reason. To have dual channel operation you would populate either slots (1 and 2- blue) or slots (3 and 4-black) if you had two sticks of RAM.
You either have to run the system in single channel or dual channel mode. You can't have slots 1 and 2 populated (dual channel) and only either slot 3 or slot 4 populated (single channel).
You should not mix the HP supplied RAM with the new stuff.
Have you simultaneously installed all four 4 GB modules in each slot and tried to boot the system? This would have both memory banks running in dual channel mode.
I have no inside knowledge on the memory controller specs for this motherboard. HP shipped the system with two memory modules in, I'm guessing, slots 1 and 3. One blue slot and one black slot had a memory module. The system was running in single channel mode. You removed memory from slots one and three and populated slots two and four. The system would not post. Chances are you must use slots one and three in single channel mode.
You also may not be able to mix different capacity memory modules in dual channel mode. So if you install three 4 GB modules and one 2 GB module the system may not post.
HP may not provide any details on how to populate the memory on this motherboard. There are general instructions available at the link provided by Malygris1.
System builder motherboard manufacturers like Asus, or Gigabyte, or Asrock give you the details on how to populate the memory slots so there is no guessing.
Jay