|The little white box you refer to will be the Modem. |
Which socket are you connecting the Modem to the router. There should be four LAN sprockets and a WAN socket. The Modem should be connected to the WAN socket. Connecting it to one of the LAN sockets will produce the symptoms you describe.
If by chance you have an ADSL router that has four LAN sockets and an RH-11 telephone socket then it wont work with cable. Whati's the Model number of this Router and Modem?