ralph scott like @mayer pointed out already, let us know what your diagnsotics LED’s are telling you.
The iMac (27-inch, Late 2009) computer has four built-in diagnostic LEDs on the main logic board that can help you to troubleshoot the computer. The LEDs are located on the bottom left edge of the logic board (under a piece of black mylar tape) and can only be seen when looking through the lower vents of the enclosure.
• Indicates that the trickle voltage from the power supply has been detected by the main logic board. This LED will remain ON whenever the iMac is connected to a working AC power source. The LED will remain on even when the computer has been shut down or put to sleep. The LED will turn off only if the AC power source is disconnected or the power supply is faulty.
• Indicates that the main logic board has detected proper power from the power supply when the computer is turned on and that logic board voltage regulators are functioning properly. This LED will be ON when the computer is turned on and the power supply is working correctly.
• Indicates that the computer and the video card are communicating. This LED will be ON when the computer is communicating properly with the video card. If LEDs 1 and 2 are ON and you heard the startup sound, but LED 3 is OFF, then the video card might be installed incorrectly or need replacement.
• Indicates that the computer and the LCD panel are communicating. This LED will be ON when the computer is turned on and video signal is being generated. If the LED is ON and there is no image on the display, then the LCD panel, the LED backlight board, or the cables between might be installed incorrectly or need replacement.
Some test points are accessible on the logic board when the LCD panel is removed. The test points are defined below.
Logic Board Test Point Function
Standby 12V power (permanent power coming from power supply and present as long as AC cable is connected, even if computer is off); corresponds to LED #1
Backlight Control pulse width modulated signal (from logic board to LED backlight board, to adjust the backlight level setting according to user setup)
12V Run-Mode power to logic board (coming from power supply, present as long as system is on or asleep); corresponds to LED #2
Power On Request signal (from logic board to power supply when power button is pressed)
Backlight Enable (signal from logic board to Backlight Controller board, to enable backlight