It appears that we have the same, or almost the same, iMac. Mine is an A1225 "iMac8,1", 24-inch Early 2008 with 2.8 GHz Core2Duo. Mine has ATI Radeon HD 2600 Pro graphics, but some Early 2008's had some NVIDIA card that was (I think) more prone to failure.
Which graphics card does your have?
Unfortunately, I don't think I can help much. It seems you've tried everything I can think of. I would be cautious about assuming that the video card is the problem, because I thought the logic board LEDs were supposed to indicate video card problems, and you say your LEDs are all OK. Of course I might be wrong and maybe some video card problems don't show on the LEDs...
If yours has the NVIDIA card, what I've read about it would make me not bother getting it repaired. Instead, I'd look for the Radeon HD 2600 Pro like mine has. I think I've seen them on eBay, but not cheap.
What you really need is someone you can
borrow a compatible card from -- to verify that yours is actually the problem. (Sorry, I can't lend you mine -- I need to use it!)
If you have the original OS X installation DVDs (should be OS X 10.5 Leopard) -- does the machine fail to boot from them, too? I see you've installed Yosemite, and that should work. (I haven't tried Yosemite yet -- currently running 10.8.5 Mountain Lion.)
If you can't borrow a graphics card, I guess you'll have to take a chance or give up.
Found this in an old iFixit web page I saved to my drive, but you probably know this info already:
LED 1 - Indicates that the trickle voltage from the power supply is detected by the main logic board. This LED will remain ON while the iMac is connected to the AC power. 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 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.