Starting up an unresponsive iMac
After a power outage or surge, however brief, some iMac models won't start when you press the power button. To resolve this issue, first locate the power cable in the back of the machine. The power cable for all newer flat-panel all-in-one iMacs can be found in the center of the machine near the bottom of the back panel. The power cable is a thick white cord. Pull the cord from the back of the iMac and wait five seconds. Re-connect the cable and press the power button.
If the machine still doesn't start up, remove the power cable from the back of the iMac and also the from the power source. Verify that the power source is active. Re-connect both ends of the power cable and press the power button again.