Unless I mis read your post, here's the deal

When you pluged your modem into your PC, the modem reconized your PC's MAC address.

When you pluged in your router, the modem did not reconize the routers mac address.

With the router in place and off, Power cycle the modem then turn on the router. Once all the lights are blinking like they normally do, turn on the pc and all should be well.

edit: most modems can only reconize one mac address