The NIC is the card that has the RJ45 cable going into it. It's either on the same plate as the one with your mouse and keyboard going into it or it's located under that plate. If it's on the same plate as the one with your keyboard/mouse, then it's integrated (built-in). If it's got it's own plate, then it's a stand alone card.
You don't have to reinstall windows to download the drivers. You have to do it from this PC, then transfer it over and install.
There's one thing that occured to me when I reread your first post. Are you sure it's the cable? Plug it into your system, and then watch the lights on the router. If the light doesn't come on, then it's the cable or your NIC. If the light comes on, it's not your cable. The light you should watch is the one corresponding to the number on the back of the router. For example: if you plug into port number 3 on the back of your router, watch light number 3 on the front. The computer must be on.