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I’ve always turn off my Imac at the end of the day, but I don’t unplug the power cable from the outlet. Yesterday the computer didn’t start at all, I’ve plugged it in another outlet , still nothing … after a few hours I tried again and it started.Like always at the end of the day , I shut it down, and today it doesn’t turn on again, I’m pressing the power button but nothing.I’ve checked the cable , the outlet , everything is placed correctly . Thank you in advance for any kind of help, suggestions.!

Remove the front bezel. There are diagnostic lights to the right of the RAM slot. With the machine plugged in try to start and observe what those lights do and let us know. Here’s how to get to it: iMac Intel 24" EMC 2111 Front Bezel Replacement

Seems like you need a new power supply.