IMac shuts down during startup

Did you try disconnecting all peripherals or starting up in verbose mode (⌘V) or safe mode (shift)? See also Apple's KB article and these qustions:

• What should you do if your OS X system fails to boot, being stuck at gray screen with the moving wheel?
• White MacBook hangs at gray Apple screen forever, won't boot to single user, won't mount using Disk Utility. What do I do next?

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.