Black screen and fan revs no chime

If it is not chiming, it means it is not passing POST checks. Try booting it with the battery disconnected. It most likely is the logic board signal ppvcore_s0_cpu, so check that out as well if you have a multimeter (you will need to get a board view and schematic for 820-3115).

Most likely is a logic board issue, possibly dead CPU or voltage leading to the CPU? Check the board for liquid damage as well, and clean if it is present (but note the areas effected).

You'll need a hardware bypass on the grey screen to permanently disable the GPU. Some software fixes work for a while, but it always comes back. You can even have the GPU reballed and it will work for a while, but overheat again and return. The only "permanent" fix is to jtag the unit using dosdude1's method. Or, you could bypass it using RealMacMod's method. Both are found in Google. I've done several and both involve, either soldering wires to pads to jtag code onto the logic board. Or, software and a jumper cable to bypass and keep the sleep function working. Either way, you're faced with making the system believe that there is no other graphics processor but the onboard intel gpu. It was an Apple recall to replace the Radeon gpu, but even after replacing it, they still eventually failed. I stay clear of that year, but MadMod is only 30 minutes away from me. So, if I do get one in, I let him do it for me for a modest price. You can buy that software on his site, but without the physical bypass, it's only a temporary fix, until you clear the PRAM or NVRAM.

As far as the top question, I’ve had luck with turning off the unit, taking the battery out. Hold down the power button for about 30 seconds, the apply power by the power supply while holding down, Continue to hold down for another 30 seconds. Let go of the power button. It should start up after you push the power button after letting go. The fans will be on high, but let it boot all the way through to the home screen, if it makes it. Then do a normal shut down, allowing it to spin and write it’s exit code. Wait a few minutes, then restart normally. The fans should spin up, but then return to the normal state. You can also start up in safe mode by holding the shift key down all the way through the boot procedure. It’s really a bad instruction set at boot that needs to be re-written (kext) from my experience. Getting it to boot all the way through is paramount in rewriting the exit code properly. It’s a trial and error thing, but that has worked for me in the past. I’ve also used the system boot USB drive, to boot from and run diagnostics on the board. Removing ram and changing the ram amount or configuration will force it to re-examine the parameters of the board and environment. This has also worked to force it to boot slow writing a new kext file to return the fans and logic board state to normal. Good luck.

In my case it was a problem with the I/O board. After unplugging the board and rebooting the computer started working.