Unless you're on a very old ethernet card (one that would support 10mbit and not 10/100 or 10/100/1000), then upgrading the NIC won't do any good. To get faster download if you're already hitting your network cap, you need to increase your service limit with your ISP.
However, if you're not hitting your current cap, then it would either be an issue with your network card, or an issue with your router. I know that after I replaced my old router, I was able to hit my download speed cap.