iMac won't turn on. No LEDs light up. iMac 27" Late 2015

I would start at the power outlet using a outlet tester to make sure its correct wired. Sometimes I've seen power supplies damaged by miswired outlets and bad or no grounding doesn't help matters either!

You don't need anything fancy, I have one of these AC Outlet Receptacle Tester

Next you should inspect the back of the systems connection where the cord connects. Sometimes I find corrosion or arcing has damaged it and I often try a spare cable to be sure the cable its self wasn't bad

Then we need to review the systems onboard diagnostic LED's and as you've already noted the LED's are not lit and shorting across the power switch din't offer any life, we need to go back and verified the AC power side is good then the issue is likely the power supply

It's not that uncommon for them to fail. The bigger risk is a power surge or lightning hit which damaged them iMac Intel 27" (Late 2012-2020) Power Supply Do make sure you have a good surge suppressor or better yet a UPS

If you do find the outlet has issues then you'll need to check the buildings wiring and also inspect the breaker panel making sure the panel is correctly wired and verify the grounding connection for the building is intact. Older building often have poor ground for the grounding rods rotting out or corrosion at the clamp.