mayer, I think the reference here is to the manual. Sounds like the OP only has 1 LED working on the iMac. All that the 1 LED shows is that the computer is plugged in and that the PSU receives power. It does not validate that the PSU is working. I would suggest to measure the output of the PSU.
Check some of the test points with a multimeter
Pin 1 Ground
Pin 3 5V power for Hard Drive(s). Note: If present, the 12V power will come directly from the Power Supply to the Hard Drive thru the power harness cable.
Pin 4 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
Pin 6 Backlight Control pulse width modulated signal (from logic board to LED backlight board, to adjust the backlight level setting according to user setup)
Pin 11 12V Run-Mode power to logic board (coming from power supply, present as long as system is on or asleep); corresponds to LED #2
Pin12 Power On Request signal (from logic board to power supply when power button is pressed)
Pin 13 Backlight Enable (signal from logic board to Backlight Controller
board, to enable backlight
"Press power button and Verify if system turns ON. You may alternately check for presence of a 12V DC signal between pin 11 and pin 1 of logic board when power button is pressed."