If it comes to replacing video card, you won't need that wire at all.
You'll remove a metal plate, which covers the access to the card's "*censored*" and the card will have its own VGA slot, which will be sticking out through a hole in the back of your computer.But the wire isn't connected to the vga slot. Its connected to something on the motherboardYou know, I'm not sure here.
I'm not really a hardware guy and even if I was, I can't know every computer model.
This is some rather unusual setup.
Without really seeing it in person, it's hard to advice.
You may need to get an identical card...

In any case, try to remove it and put it back.
That's the first step, no matter what.Even a picture here doesn't show me connections:

Alright thanksSure thing Hey Broni, I was going to search to see if there was anything to help for taking out the card, but while I was searching my screen went black, and seconds LATER it said there was no vga input. I CHECKED if everything was connected. (they were) Does this mean that my GRAPHICS card is officially dead?
I am CURRENTLY on my older computerIt's getting more likely so.
Still, try to re-seat it.Oh wells, I bought a new graphics card today and installed it sucessfully

Thanks for all your help Broni!!
If problems start to appear again, I'll be back to haunt you.
Thanks again!!!You're very welcome