iMac won’t turn on
It’s been at least a month since my iMac hasn’t turned on even after unplugging it and plugging it back in. I was using it as normal and all of the sudden the screen goes black and didn’t start up again.
iMac 27″
Try another socket or if you are using a power strip, especially if it's 5+ years old try plugging directly into the wall. You don't mention the model year so it's a little difficult to offer any help and you make no mention of any troubleshooting other than unplugging and re-plugging it back in.
So, please follow the steps in If your Mac won't turn on