I believe your unit does have the 8800GS
Can you run an ext display? If so does the problem continue on the ext display?
If so then VGA or logic board are possible causes, if not then LCD may be cause.
A repeating bong sound at boot may indicate a RAM issue??
Have you got iStat widget installed? What are the VGA/GPU temps like?
Are your fans running? what speed?
If it will boot after sitting overnight then perhaps it is a heat issue...
Are you willing to take front bezel off and look at the diagnostic LEDs? They may help isolate the problem
Bezel removal
LED #1
• 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.
LED #2
• Indicates that the main logic board has detected proper power from the power supply when
the computer is turned on. This LED will be ON when the computer is turned on and the
power supply is working correctly.
LED #3
• 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.
LED #4
• Indicates that the computer and the LCD display 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 LCD display panel, the LCD display panel or inverter might be
installed incorrectly or need replacement.
IIRC, The LED's are on the logic board to the right of the memory slots and above the HDD SATA connector. The SATA connector is a right angle connector so may obscure them a little. They are surface mount and look like little white squares when OFF and green when illuminated
LED location
HIH