Can you tell us i it is a blank black screen or is there any writing on it?
Can you press and hold down the power button on your iMac till it shuts off, Once you have done that can you then find the Command, Option, P, and R keys on your keyboard.
Once you are ready can you turn on the machine and then press and hold the Command+Option+P+R keys at the same time and hold the keys down until you hear the startup chime 3 times then let go of the keys and let me know if the machine will now startup properly or if you still have the blank black screen.
When you press and hold down the power button does the Mac turn off and does the screen appearence change at all or is it the same black screen, I am not sure if my question will make sense, however I am trying to find out if the screen seems to power up.
If the screen seems to dim when you turn the machine off can you then disconnect everything from the iMac and remove the power plug from the machine then press and hold the power button down for a full 30 seconds then reconnect the power, mouse and keyboard only then wait 5 seconds and let me know if you can now startup and press Command+Option+P+R like before till you hear the chime 3 times.
If nothing happens can you tell me what does happen when you try to power up the machine?
Let me know.
This will sound stupid, However when you try to power it up does the screen look like the black is lighter as though the screens backlight is lighting up?
If you can power it off then turn off the lights in the room and then power it up can you tell me if the screen seems to glow?
Can you power up your Mac and then wait about 2 minutes and look very closely at your screen and let me know if you see a shadow of a display, Either that or take a flashlight and see if you can see a ghost image on your iMac's screen and let me know
Has your Mac been acting strangely at all recently?
If not can you tell me what model of iMac it is?
Can you look on the base and let me know if you see a model number like M9290LL/A
If not can you confirm it is the model with the white domed base?
So it looks like this
Is that correct?
In that case there is only one other thing we can try to check, So can you tell me if you have an external monitor and a video output cable for your iMac?
If so can you power off your iMac and conect the external monitor then power it up and let me know if you see anything on the display.
This way we can see if it is the graphics card that has failed or if it is the LCD that is having the issues.
Let me know what happens.
Do you have another Mac and a firewire cable?
On the problem machine can you shut it down then wait 5 seconds and power it back up and immediately can you press and hold down the T key for about 1 minute so the machine will hopefully open in target disk mode.
Then can you then connect the firewire from the problem machine to a running mac and the hard drive should mount as an external drive and show on your desktop.
Let me know if the problem Macs drivve mounts on your desktop or not as this will tell us if the LCD has failed or if it is the graphics on the logic board.
In that case it would indicate that there is a possible issue with the graphics or with the main logic board on the machine, The trouble is that there is very little more we can do in this format to help you troubleshoot beyond this point.
Honestly the best thing to suggest from here would be to take it to your local Apple store and have them troubleshoot the hardware for you as the only other option would be to change out the logic board and graphics which can be rather expensive and involved.
Let me know what you prefer to do.