Mac won’t turn on.

What year is that 27" iMac?

Pull the plug from the back of the machine and reinsert it firmly.

Make sure you're plugged into a wall outlet and not a power strip.

Follow this procedure to reset the SMC:

Desktop computers -

1. Shut down your Mac, then unplug the power cord.
2. Wait 15 seconds, then plug the power cord back in.
3. Wait 5 seconds, then press the power button to turn on your Mac.

Mfawks Said:

"Mac won’t turn on: My Mac won’t turn on? Have tried the online troubleshooting with no avail? Any advise? TIA"

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Refer to this site: If your Mac won't turn on - Apple Support

Or....

Contact an AASP (Apple Authorized Service Provider):

1. Go Here: Find Locations - Apple Authorized Reseller
2. Click: Service & Support
3. Enter: your location information
4. See: if there is an AASP nearby
5. Contact: an AASP that shows up, and find out more about the services that they offer to fix this iMac