I guess I dont fully understand the details on why exactly you changed ISPs or have to buy more addresses but I do know a few tidbits that might help:
1. you didnt have to have 2 separate addresses when you used a router because to any outside network your xbox and computer were the same destination and the data was "routed" to the correct device once it came in your router
2. to find your computer's IP you can type "ipconfig /all" in the Run box from the start menu OR you can just go to
www.whatismyip.com where it will instantly tell you your address using magic and the miracles of modern science
My first guess is you've got an address error somewhere. After that I would check your cabling.