iMac won't turn on, especially with RAM sticks

IF your system was not working from the get go, I’m suspecting the power supply has failed given the onboard diagnostics

Here's a breakdown of the onboard diagnostic LED's

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.

So clearly the lack of LED #2 tells us we need to focus on the power supply first. Its also possible the logic board has a problem as well. I often find power surges and lighting strikes kill both. Are you using a good quality surge suppressor? Or better yet a UPS? Did you check the outlet to make sure the ground is properly wired and at the breaker panel make sure the ground line from it is properly bonded to either a copper water pipe leaving the house or one or more grounding rods.