Hi!
If you really want to be sure what is the problem....
You'll need help to do this... Open you iMac and just lean the lcd to be able to blow the power supply section with your hair dryer and eat ONLY the power supply section .... ( Ask some one to keep the LCD in place...) When heating press the power button some time and when the power supply will get enough heat it should start... It is able to get a lot of heat but don't melt anything too...
This is a temporrary fix to determine and isolate the problem. Once you are sure that is the power supply.. Replace it!
Enjoy!