Will not power on. Tried everything. HELP

iMac intel 27” EMC 2429 Mid 2011. Hadn’t started it in maybe a year, it had been plugged in the whole time. Went to start it…dead as a doornail. No sound, nothing on screen. Believe I’ve tried everything, including: hold button 10+ sec; unplug power cord from wall for a minute; held button for a minute; (yes..cord is good—even tried the cord from my NEWER iMAC…did continuity check on the cord, checked voltage in the cord end); power button feels like it’s working fine (tactile feedback). So…that was all the stuff on the “outside”. Then we cracked the case to check the LED’s. Power plugged in, LED 1 blank; hit power button no change (all blank). WHAT NOW? Help and thanks in advance!