Chosen Solution
The error message from diagnostics suggests the fan has busted apparently but mentions the HDD. Just white screen and boot load progress that never gets further than half way. Note that i can still SSH to this machine over wifi and ethernet just fine and have backed up the HDD doing this. There is no guide on this lovely site for replacing a fan it seems (other than the optical drive fan). Cannot understand why it would perform fine over SSH but not boot to gui logon! None of the key combinations work to get to recovery screen.
The diagnostics error is pointing to a fan which is under the logic board that forces air across the HDD iMac Intel 27" (Late 2009-Mid 2011) Hard Drive Fan
Sadly, we don’t have guide to pull the logic board, this guide will get you mostly there Installing iMac Intel 27" EMC 2429 Dual Drive Kit (HDD or SSD). Once you get to Step 32 you’ll need to disconnect the last cables to fully remove the logic board. The white screen issue is a GPU board failure! You’ll need to pull the GPU board off, see if cleaning off the old thermal paste and pads and refresh both allows the system to work. Here’s a bit more on the GPU board from the 2010 model iMac Intel 27" (Late 2009 or Mid 2010) Graphics Card Replacement Pick it up at Step 11 after you’ve taking the logic board out. Some people have managed to get the board to work again after cooking it. While that might get you going it maybe short lived. In any case you’ll want to monitor your systems thermals and not push the graphics too hard as that’s the issue of this series as more modern graphical apps over stretched the the GPU. I would strongly recommend using this great app for that TG Pro and turbo the fans.