From the troubleshooting procedure you describe ,I'm kind of at a loss.
I had a monitor do this , it was the db9 connector on the monitor (bad solder).
----
Yes a 'source' signal line can cause hardware failure if say , one of the signal lines got shorted to say , +12v.
The only advice I can give , is to use the new video card , with all new adapters/cords , and another monitor ( if you can get one. ).
That 'should' eliminate everything downstream of the video card....if it still does it , it's down to motherboard or BIOS....