Well thats a decently complex question, it depends on how your modem is configures, how your ISP handles things, and a few other things. Its probably PPPoE or some other simular type, which is a fancy way of saying you need a password to get online, while with cable you don't. You can decide (sometimes) which device handles that authentication process. Sometimes its the modem, sometimes the router, or sometimes you can even install software on your computer that does it (not possible in this case ofcourse).
Start by calling Century link and ask
1. Whats the model number of your modem.
2. Is there any username or password you need to access it.
3. Is it possible to put it in bridge mode (also known as transparent).
4. Do they have a list of closed ports?
I tried looking on their support site but yea...I couldn't find anything there even talking about High speed internet or DSL. Just dialup. Hopefully their phone support is better. ::crosses fingers::