iMac Black Screen & Loud Fans

Led 1 means that the computer is receiving a source of power. When this is on the computer will be plugged in. LED two goes on when the computer has constant power and tries to boot up. Now here is the problem that you are having, LED 3 isn't on which suggests a video related issue. LED 3 means that video signal is being generated. If this LED isn't on then the computers graphics card has failed. This means that you can do one of two things. One, you can try a video card reflow(google it), or two, you just need a new logic board. The only sure way to fix this is with a new logic board. Sometimes the reflows will only work temporarily. Unfortunately this is the only thing that you can do because that is the only problem related to not having LED 3 on.

Hope this Helps.