You're going to need a router because the Xbox will have to connect the DSL modem just as your computer does. The router is like an extension plug in that it allows more than one device to hook up to your DSL modem.
If you want to keep your XBox where it currently is, then you're going to have to buy a long ethernet cable to run from where the modem and router are all the way to your Xbox's location. Instead of doing that, I'd recommend buying a router with wireless capabilities. Then you can buy a wireless receiver to hook to the Xbox without having any long cables running through your house.
Here's what I'd recommend if this product is available near you:
http://www.linksys.com/products/prod...id=35&prid=601 <---- The router
http://www.linksys.com/products/prod...id=558&scid=38 <---- The wireless receiver to hook up to the Xbox
I have our PC connected with a Linksys wireless receiver and the router is in my room and it works great.
And yes, you'll be able to use Xbox Live and the internet at the same time.