What version of windows are you using ?
I hope u used the modded bios with the same bios number what you originally had on your card
If you using modded bios with different bios version number , you have a chance to kill all your gpu's !!!
Do you have automatic updates enabled on your computer ?
check if you get some unwanted updates .
use  DDU, remove the drivers
plug in the non working card let see what  happening

"I turned off the rig, disconnected the other two cards, connected HDMI to the card, rebooted..

Upon booting into windows, fans spin for 3 secs, screen flickers then turns to normal for 3 seconds.. REPEATS for 3-4 times.. then display stays on!"

So you have problem to boot into windows ? can you see the bios post ? can you boot into your bios with the bad card and monitor connected to the  "bad" card ?