One other thing you can try is cloning the MAC address of the computer to the router. There is usually a setting somewhere in the router administration which will let you do this, or at least manually enter it.
Cable internet identifies you via your mac address so they can know who is authorized to use their network.
You have 2 options:
1. Get your router to clone your pc's mac address. From what you are saying it seems TW provisioned your pc's mac address. Like druidcent said, there is a setting on your router.
2. call up time warner and have them provision your router's WAN mac address. If you ever need to replace your router, you'll need to have TW to reprovision your new router's mac address.
From my experience with cable internet, option 1 is better as it make swapping routers more convenient.
You might want to upgrade your router in the near future to take full advantage of your internet connection. I used to own that router and the WAN -> LAN throughput was not that great. (sorry don't remember hard numbers as it was a long time ago)
Hope this helps!