Will not fully boot

Yikes, sorry to hear about the issues! Have you tried booting in target mode from an external hard drive/computer to see if either the drive or the drive-related components (cable) are the issue? Have you tried using an external display to absolutely rule out the video issue (no external video would mean there is a video issue)?

I have had a few Pros exhibiting a "slow booting" problem sort of like this, and the problem was resolved by replacing the DC-in/sound board. In most of these cases Firewire was also not working. Since a logic board replacement didn't fix it, the only other major component is the DC-in/sound board, so it might be a logical next step to replace that.

Good luck!

Being nowhere near an expert, I studied your question for the challenge. Are you trying to establish if it's the graphic chip that's causing the screen to go black?

My old 12" MacBook could be used as an external drive to an other Mac if connected through fire wire and "t" pressed during start up. Just thought there was a possibility that it could be used to rule out something(?). (i'm not sure if the procedure has been changed, but I suspect you'll know)

try to reset it using fn+control+shift+power button . press all simultaneously, when system start butting press alt/option too while holding those buttons, this should turn it of. after what push the power button to turn it on. after system full butting, turn it off and do SMC