You can glue the pin back but the problem why this happened also needs to be solved too. I am not sure which pin is it, it doesn't seem like a power one which makes me wonder how can such a pin burn up... Chances are someone managed to put the card in backwards in the PCI slot for whatever reason and this likely permanently killed the card and the motherboard involved.

The story goes like this: I agreed with the seller to pick up the card personally since it was a local sale. During my trip to the seller, he, according to his statement, had difficulty removing the card from the system, because it wouldn't budge, so he went medieval on it - pulled it out with too much force. When I got to him, he explained to me what happened, and gave it to me for free. I took the card and give him some symbolic tip for a coffee or something. However, I am really sad about the card. He did mention that the card is probably burned. But I don't know how can that be, if he only removed it by force. Right? The card visually looks OK.

seems to be the reset pad that's torn loose.