If you are not seeing bios, it will not matter what drive or OS you install, something has been damaged. Bios are what initialize and start the hardware to boot the os, that is it's purpose.
The question is if it's the cpu or board, I think a part swap is the only way to properly diagnose which it is, but I have a pretty good idea which is the problem.
My bet is that its the motherboard, while CPUS are not hard to damage, odds of destroying the graphics system in it is pretty slim. More importantly, you cannot write to the cpu, so unless it was completely burnt out I would imagine you would get some sort of gibberish and artifacts on the screen. The odds of burning out the GPU perfectly to the point that the board doesn't recognize that it's there at all is pretty slim, especially doing so without impacting the rest of the processor. Possible, yes, but the odds are up there, may as well buy a lottery ticket. Also, a processor that has a problem usually gets worse and worse over time. It's rarely a case of this part died and the rest keeps working fine.
So for me, it points to the motherboard. Something in the chipset is damaged and it's simply not detecting the onboard graphics in the processor which is why it will not boot. The system thinks you have no video system installed. If you use a speaker you should get a beep code telling you no graphics card detected, just as you do for not installing memory.
Also you cannot use Grub to enable onboard graphics, there maaay be an EFI call for it, but it's unlikely. Most bios have an IGPU, PCIE and auto, if you set the bios to auto the system uses both but sends the initial signal to pcie. This will allow you to detect it in an OS. Nothing is going to detect it in an OS if it's set to pcie in the bios because the board should disable it (not all do, but most do).
By the way, the solution I posted made sense based on what you wrote.