Which OS are you using? And more importantly, what is on the other end of your Ethernet cable? I've got the MA790FXT-UD5P which is really a go faster version of your board. It has twin LAN connections, which is to all intents and purposes what you have but installed twice. I found the drivers supplied on the CD that came with the board work fine for Windows XP whilst the default drivers for Windows 7 work fine with that. In both cases I get a reported connection of 100Mbps, which is what I expect as I'm connected to a 100Mbps Ethernet switch. I can't test it at gigabit speeds as I don't have any gigabit kit to check with, but I don't see any reason why it shouldn't work.
I expect you have found the same problem I did with the 'latest' drivers. In both XP and 7 the updated Realtek drivers do not work. I have tried under both, and ended up rolling back in both cases to get a connection again. My suggestion here is to avoid the driver available through Windows update and watch the Gigabyte site for updated drivers instead.
100Mbps should not limit your internet connection. The fastest available I know of without resorting to extremely expensive dedicated connections is the 50Mbps service from Virgin Media, which means your current network connections is running at twice the connection speed and shouldn't be a problem. Even if your service was a 'mere' 10Mbps I doubt you would notice the difference much as most of the bottlenecks on the web now seem to be at the server end where they simply cannot get serve the pages or stream the data fast enough. As things stand I see no real need for a connection faster than 20Mbps unless you regularly use a site or download from a server with a guaranteed high connection speed.