There was an option to clone the mac of a network card in your pc in your router. If you had a network card that has never connected directly to cc than you could have cloned that mac on your router. I cant answer your question about your subbed modem as I have not got as far as you yet.
When you connect to your Dlink routers config, on the home page select the wan tab on the right hand side of the screen, at the bottom of this page you should see a section called, Dynamic IP, here you have the option to clone the routers mac address, or enter a mac address of your own. I think by default this field is left blank. So either try it with the routers own mac in the box's, or enter your own.