the wire connect the dvi pcb support ? dont know why, unless the ground is not common, remove the remaining pins with a fine cutter, they may short, if the hdmi doesnt work that could be another problem
removing dvi, it's a joke and change nothing, just create problems
try to find display port to hdmi cable it will be fine ...
but personally i would toss the card, hs was removed, you need to redo all the compound pad and or add thermal grease