Hooking up xbox live via ethernet cable?

I just recently received broadband internet access. The modem I received is a Motorola Surfboard. It only has one ethernet port in the back which I use to get internet on my computer. I decided to get xbox live and instead of constantly unplugging one to plug in the other, I got a T splitter to give me two ports instead of one. Now when I do this and try to connect to xbox live, I can not do so. I do not see what the problem is and why it is not working. Any body have a clue how I can do this?