How do I turn on my iMac- it is acting as if it has no power even though it does.

Sounds like your power supply might be dead.

How did you test the wall outlet to make sure it has power?

Is it plugged into a power strip? If so, did you try changing which outlet in there it’s plugged into? Or pressing the breaker reset on the power strip?

take the battery out and put it back in again

No battery as it is a desktop, will try to borrow a friends power cord and test that possibility.

Thanks!!!

Sadly nothing is working. I think it is the MPU and have made an appt at Apple.
(In the past it has required me to unplug the computer wait then plug in again to start.)

Sometimes it looks like it’s off, but it is just in a perpetual sleep. Hold in the power for 10 seconds, and if it was on, it would now be off. Hit the power again and listen for the chimes.
If it was off and you’re getting no power, sometimes resetting the power manager helps. Check out these instructions for resetting the System controller and for some other tips you can try first.

@simpleD Thanks for the input. No chimes. Nothing actually.Thanks so much for the info. Perhaps it will help someone else with a misbehaving computer.

I took it in to the Apple store.

For those who might find this question in the future this is what they said:

It is most likely the power controller- located in the upper right corner of the computer. I might also be the logic board.

They ordered the parts- I had purchased the extended warranty and it is all covered but I will be sans computer for up to a week.

Gee- I may actually get some painting done… :)