This may take some trial and error to find the problem. Resetting the SMC - First unplug the unit and press the start button for 5 seconds. Next try a PRAM reset, hit the start button and immediately hold down the Option & Command and P and R keys wait till you hear it tone three times. Next re-seat the RAM, here's how: iMac Intel 20" EMC 2133 and 2210 RAM Replacement
This failing you will need to open it and examine the diagnostic LEDs:
Here's a video on how to open it up:
http://www.youtube.com/watch?v=8Xs_1QCyP...
You will need suction cups:
Heavy-Duty Suction Cups (Pair)
and a Torx screwdriver set, here's what I use:
[produto vinculado ausente ou desativado: IF145-022]
LED Startup Sequence
LED #1 = Power available.
If no LED is visible:
• Verify AC source
• Verify known-good AC cable is connected
• Verify cable connection between AC inlet and power supply
• Verify cable connection between power supply and logic board
• Verify power supply
LED #1 + LED #2 = Power available, and system is powered on.
If second LED is not visible when power button is pressed:
• Verify power button connection to logic board
• Verify power button functionality
• Verify cable connection between power supply and logic board
• Verify power supply
• Verify logic board
LED #1 + LED #2 + LED #3 = Power available, system is powered on, and video card found.
If third LED is not visible after power on:
• Verify that MXM video card is seated properly
• Verify logic board
LED #1 + LED #2 + LED #3 + LED #4 = Power available, system is powered on, video card found, and internal LCD found.
If fourth LED is not visible after power on:
• Verify cable connections between LCD panel and logic board
• Inspect LCD display cables for cable damage
• Verify external video functionality, and according to result check the following items:
-If external display works then verify/replace LED backlight board
-If external display works then verify/replace LCD panel
-If external display does not work verify/replace logic board