IMac 27” mid-2011 stuck on startup (grey screen)

Disk I/O errors literally translate to input / output errors, which occur when the system is unable to communicate properly with the hard drive. This is very indicative of a hardware failure, whether it be with the hard drive itself, the logic board or the SATA data cable that runs between the two. Given the age of your Mac (5~ years) I would assume that the hard drive is to blame. Disk Utility repairs the volume on the disk at a software level, often it will report when hard drives have a hardware failure but there are also times when it repairs correctly despite communication errors still being present.

Apple Hardware Test (AHT) IS pretty good at giving you a solid answer but as you've found out it's no longer on your hard drive, likely lost during an old upgrade or re-install. You should be able to boot to it using the gray restore discs that came with your iMac. Discs from another iMac/Mac will not work unless it's identical to yours, these are very hardware specific. AHT should be on the disc labeled "Applications Install DVD", with a small mention of AHT and its version number. Holding down D while booting with that disc inserted should boot the Mac to AHT.

Solved: Booted to Single-User mode and disabled Radeon GPU.

Details of investigation:

Initially I suspected hard-drive corruption and went about trying to remedy that. Unsuccessfully, I tried the following, with each continuing to hang as described above:

• Safe boot
• Boot into recovery (including Internet Recovery)
• Boot from install media on USB drive
• Boot from OS X installation on USB drive
• Clear NVRAM
• Reset SMC

I also ran the Apple Hardware Test many times without it finding any issues.

Verbose safe boot (Cmd+Shift+V) output everything that I'd expect to see but would then hang as described above.

After coming across more posts online of GPU related problems I revisited this as the cause:

• https://discussions.apple.com/message/22751155#22751155
• https://discussions.apple.com/thread/4766577?start=210&tstart=0

Attempting to boot Ubuntu from a USB flash drive, I could only get as far as Grub. When trying to boot Ubuntu Desktop or run the graphicstest in Grub the system would hang.

At this point, running Apple Hardware Test hung right before the end of the standard test, possibly [guessing] when doing a video test.

Based on the advice in the Apple Discussions posts above I did the following:

• Boot into Single-User mode
• Execute the following commands:

    /sbin/fsck -fy /
    /sbin/mount -uw /
    mkdir /Disabled_System_Library_Extensions
    cd /Disabled_System_Library_Extensions
    mv /System/Library/Extensions/ATI* .
    mv /System/Library/Extensions/AMD* .
    touch /System/Library/Extensions
    exit

This time the machine booted all the way through. However, graphics are extremely slow, even just transitions when minimizing windows. I will be taking my MBP to Apple to demand a replacement as the large number of reports of others facing similar issues makes it look like a recurrence of a similar GPU-related failure that resulted in them doing a recall.