Why won’t it turn on

What have you tried? What happened? Would be good starters!

Did you review the guides we have? The most important is this one! iMac Intel 27" EMC 2546 Display Replacement without the proper tools and techniques you risk damaging the display trying to even diagnose what has failed here.

Following the guide: After you have carefully lifted the display off, but haven't disconnected it lay the system on its back after first using some painters tape, taping the top edge down so you can raise the bottom to look inside without harming the display cables.

With the computer plugged in and the power button pressed carefully lift the bottom edge to look inside just to the left of the Apple logo you should see four diagnostic LEDs, are any lit? Counting from the bottom tell us which ones are lit.