MacOS – Freeze after “VM Swap Subsystem is ON”

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.

Your problem seems to be bit deeper since you tried few options already.

You might or might not have the recovery installed!

You could get one and use it from USB, or if it happens so you might have bootable os on USB.

In none of the above is possible then try using the Target disk mode.

For that you will need a second mac (not many have that).

To some degree the Apple Hardware test could detect problems with hardware.

Press and hold the D key before the gray startup screen appears.