Short answer. You need to visit a repair shop or an apple center. I don't have much experience with Macs but asking a close friend that does he told me the following:
If Led 1 4 and 5 stay off, that means that there is a hardware problem.
Led 1 = off with AC cable connected means that the power supply/board is probably faulty. Try to unplug and plug back but probably won't work.
Led 4 = off. Check with the external display port and a 2nd monitor, if it works and you can see MacOS. If you do, you need an LCD replacement. If not, you need a board replacement. Make sure you check the LCD internal cables.
Led 5 = off. Assuming Led 1 will be back on, Verify the internal DisplayPort cable and backlight cable connections between the LCD panel and the logic board. Check with a flashlight to see if the LCD is on, but has no backlight. If you can see anything (like the login screen) even faint.
Remember, as long as Led 1 is off it may affect how the monitor works, and the more you use a faulty power supply/board the more you risk damaging the Mac even more.
For more info, If you have experience with electronics, you know what to search for but good luck finding replacement parts to test. I would still advise taking the iMac to someone that knows of Macs or to Apple itself.
I will leave this thread open in case someone can help more but remember, we are a torrent site that sometimes offers help with software specializing in PCs/Windows. Maybe searching in an Apple focus forum would help more.
) . think of it as going to a car mechanic and asking for health issues.
