If you have a computer in your room that is connected to the internet, you can run an ethernet cable from your xbox 360 to the computer to use it's internet connection. Just enable internet connection sharing on your computer.
Go to Control Panel > Network Connections. Right-click the connection that you use to connect to the Internet. Click Properties. Click the Advanced tab. Under Internet Connection Sharing, select the "Allow other network users to connect through this computer's Internet connection" check box. Click OK. Click Yes. Turn on your XBox and connect to XBox Live.