Can you check if you get any indication of power?
Make sure that the outlet or power strip that you use actually has power
Unplug your power cord from the back of your iMac.
Wait 15 seconds, then plug the power cord back in.
Wait another 5 seconds, then press and release the power button.
Do you hear the fans start turning? Do you hear the boot chime sound? Any other indications that power is on, such as the screen lighting up?
Do you hear any error beeps?
If you have a wired USB keyboard, you should see the Caps Lock key light when you press that key.