Please try and follow these steps:
Check power connections
Make sure that your power cable is undamaged and plugged securely into your Mac and a working electrical outlet.
If your Mac has no built-in display, make sure that your external display is connected to power, connected to your Mac, and turned on.
Press and hold the power button
Press and hold the power button on your Mac for about 10 seconds. (Every Mac has a power button. On laptop computers that have Touch ID, press and hold Touch ID.)
Then press and release the power button normally.
Unplug accessories
You could have an issue with one or more accessories or their cables. Unplug all accessories from your Mac, including printers, drives, USB hubs, and mobile devices. Then repeat step 2, above.
If you see something on your screen
If your screen shows a flashing question mark, circle with a line through it, or anything else, your Mac is turned on but isn't starting up:
If your Mac turns on but doesn't start up all the way
If you see nothing on your screen
If your Mac seems to be turned on but the screen remains blank, the issue could be software related:
If your Mac starts up to a blank screen
Reset the SMC (Intel-based Mac only)
If you're using an older, Intel-based Mac, resetting the SMC might help:
Reset the SMC
Contact us
If your Mac still doesn't turn on, contact Apple Support.
After that: opening up an iMac is not supported, but for the mid 2011 you can try and remove the RAM memory and put only 1 RAM back in to see if that solves the problem.
I had this happening with my 2013 iMac last month and here it was the power supply unfortunately
