Mid 2011 iMac White Screen no boot

Hello,

This post details my attempts at fixing a Mid 2011 27-inch iMac 12,2.

When I try to boot it to the regular hard drive, it loads about 70% of the way on the white screen with the Apple Logo and progress bar, and then the screen turns black for half of a second, and then turns to a white screen and stays like that forever. When I press the caps lock key while its still loading, the iMac is responsive, but when I press it after it gets stuck on the white screen, it is unresponsive.

When I try to boot it to a properly set up USB installer of El Capitan, it does the same thing. When I try booting it into a USB installer of an older OS, specifically OS X 10.8 (Mountain Lion), it does the same thing, but instead of a white screen, the screen turns black with vertical blue stripes. When I try booting it into a DVD installer of OS X 10.6 (Snow Leopard), it gives a Kernel Error, telling me to shut down the computer, on a faded gray screen. I suppose this is because it will not load any software released before the computer itself (the mid-2011 iMac was released after Snow Leopard and originally ran Lion or Mountain Lion).

I have already tried resetting both the NVRAM and PRAM, neither of which worked.

I have already tried switching the hard drive to a different one that I set up with a copy of El Capitan, and it does the same thing.

I have already reseated the RAM in multiple configurations.

When I boot in safe mode, it does the same thing (screen turns white and never fully boots up).

When I boot it into Internet Recovery through an Ethernet cable, it does the same thing (white screen).

When I boot it into Verbose mode, it gives an error at some point that says "BootCacheControl: Unable to open /var/db/BootCache.playlist: 2 No such file or directory" and then lists a ton of Errors, before turning off.

When I boot it into the Apple Hardware Test through the Ethernet, it runs until it encounters a Temperature Sensor Error, which is because the Hard Drive I have replaced the original with does not have the same built-in sensor as the original, and since it has been previously replaced, I do not have the original hard drive with the temperature sensor. I know that this is not the main problem, but it does prevent the Apple Hardware Test from being able to fully run past this error, not allowing me to check anything but Memory first (it never gets to the Logic Board tests).

This gives me only one option: Single User Mode. I can boot into it successfully, but when I run fsck -fy it always fails, but I know there is no issue with the hard drive because I have already replaced it. I have tried to repair it with "/usr/libexec/repair_packages --repair --standard-pkgs" after mounting it as write-able and it changed nothing.

I suspect that the problem is NOT the logic board because of this statement Apple issued regarding a firmware update for this exact iMac model:

iMac (Mid 2011): Unresponsive white screen on startup or vertical lines on screen - Apple Support

The symptoms described are exactly the same as mine, but the article never goes over how to actually install this firmware update without being able to boot into the computer at all. I have tried to do it from a USB by downloading the installer onto the USB, and accessing it through command line in Single User Mode, but the computer has no actual way of opening the .pkg file other than just looking at it's contents.

The last thing I tried was installing the updates from apple through the terminal, with the "softwareupdate" function, but Single User Mode for some reason cannot access the ethernet network. When I ping any valid IP, nothing is returned, but I know that the Ethernet network IS working because it can access it properly when I run the Apple Hardware Test. When I check the settings with ipconfig, there is no DHCP address that shows up.

I suspect that the issue really is the need to update the firmware, since it seems to not be able to set up the GPU properly.

Any idea how I can set up the Ethernet connection to work through the terminal in Single User Mode, so that I can run the software update, which will hopefully update the firmware? Any suggestions of what else I can try that I have not already tried (other than bringing it to Apple)?

Thanks