If you don't know the make and model of your network card then you are going to have to open the case and take out the card and see if it’s written on the card itself. Then go to the manufacturer's website and download a driver for your version of Windows. If it’s a built in network card then it will be harder since you will have to find the motherboard make and model and do the same thing. Some motherboards mark this information on them and others make it harder to find. Just make sure you unplug the computer from the wall first.
If it’s a name brand computer like a Dell or HP then you can usually find hardware drivers by finding the model number or service tag number like in the case with Dells and then going to their website to get a listing of drivers. Since you can’t get online you will have to do this from another computer and copy the drivers to a CD or flash drive.