I have been watching the thread, but don't like to interfere with Trouble's suggestions, since he is the expert. I don't have any experience with WANs for the overall network, so maybe just deal with getting you to the router.
Perhaps some things to get back to basics. Anything you have already done after connecting directly to the router is probably not necessary to do again. And I will more than likely suggest some things that have already been suggested.
First keep the computer plugged directly into the router and loose the X-Box. After doing this, in the Network and sharing center, do you show any type of network, like a house and where is the red X? If you could attach a snipping tool picture of the Network and sharing center and use Paint to remove any personal information, it might help.
Anytime in here you might do the ipconf process to see what your addresses are showing. On a home system, the DHCP server and Default Gateway, and DNS server are usually the same. In my experience, the real DNS server is kept on the router, along with other settings for the overall network. I don't really know what is required for Workgroup names, but I keep mine all the same.
So, unless someone has changed the address of the router, and it can be done, you should be showing 192.168.1.1 for your IPv4 stuff, and your address should be a 192.168.1.xxx of some variance. As Trouble mentioned, checking the information on your roomate's system would confirm. If you are showing some different type numbers, you can enter the addresses yourself to test. And I did see your earlier attachment with the different DNS server address.
Try to use IE to reach the router. If you can't get to the setup page, try pinging the router in an administrative command prompt. If you can't do that, try pinging 127.0.0.1 and can you ping the address of your roommate?
Anyway, maybe something will reveal some info to help..If the router is not being used as a normal router, I am not sure what the addresses should be.