Hi michellez400, welcome to T3G!

The G as displayed on your screen should only mean that you're in a GPRS coverage area, i.e. the whole network! It just shows that you can use GPRS should you need it, it doesn't mean your connected to the internet. If you are connected to the net I'd imagine there's another icon of some sort, a globe perhaps, or some little arrows going in and out from the icon of Earth? Can't quite remember what the Samsung does!