Chosen Solution
When load progress half done iMac shuts off. No keyboard, mouse or optical drive response. The logic board is getting power. Hard drive and fans run. No keyboard or mouse response. I tried disconnecting AirPort, video cards and optical drive and still have some issue of shutting down after a minute
I would try removing all detachable devices such as hard drive, usb hubs, camera cable, wifi card, keyboard, mouse and any other connector except the monitor. Then try running the mac and see if the computer shuts off after the same time it does when the hard drive was connected. If it doesn’t, try using a different hard drive with OSX installed and see if that’s the issue.
What does the onboard diagnostics LED’s telling you? Locate the tape covered LED’s
What do you see?