You should edit this
I have similar issue with my 27 iMac 2013 model, it was working all fine after ssd drive upgrade (done 100's) and it stopped working. I tested another working power supply and it won't turn on and no LED's are on. I tested the power supply thinking it was faulty but it work's fine on another machine. When I put my ear to the PSU I can hear electricity but on pressing button nothing turns on, tested few other cables and still no LED lights. Could the logic board be fried as there was a lot of dust when I cleaned it from the previous owner during the SSD drive upgrade.