My iMac doesn't power on?

paracelimota, here are the Deep-dive instructions for your model from Apple :"

1.Power ON system. Verify if there is any indication that the system has powered up (fan rotation, hard drive or optical drive noise, backlight turns on).

If yes:The symptom is powering up.

If No: Go to next step.

2. Remove front bezel and locate diagnostic LED’s on logic board.

Plug power cord into system. Verify whether diagnostic LED #1 turns ON.

If yes:Trickle voltage being supplied by power supply. Go to next step

If No: replace power supply.

3.Press power button while monitoring diagnostic LED’s. Does diagnostic LED #2 turn ON and remain ON after pressing the power button.

If Yes:Power supply functioning and logic board detects supply voltages.

If No: go to Step 5

4. Disconnect power then remove power supply and carefully inspect AC inlet and DC output connectors and cables for damage or poor connections. Were any problems identified?

If Yes Replace damaged part.

If No Go to step 5.

5. Inspect power button and verify that it is properly connected to the logic board.

If Yes: Visual inspection OK.

Go to step 6.

If No: Reconnect power button.Replace rear housing (which includes power button) or logic board if damage is present.

6. Disconnect power button from logic board and verify continuity between two pins when power button is pressed.

If Yes: Power button is functioning correctly. Go to step 7.

If No Power button faulty. Replace rear housing which includes power button.

7. Press power button and verify whether system turns ON.

If Yes:Power supply is functioning.

If No: Replace power supply. Retest.

Remember, I am not a Mac person, just a person who enjoys hardware from any manufacturer. Hope this helps, good luck.