Most cable modems only permit one ip address and they bind it to the mac address of the device it's connected to. In your case it's currently your router. If you want to go direct from the modem to the pc, disconnect from the router and power off (unplug) the modem for 5 to 10 minutes. This should be enough time for the modem to reset itself and then plug it directly to the pc... Power up the modem, give it a minute or two to sink with your provider, and then turn on the pc. That should do it.
EDIT: Don't expect the modem to be identified by Windows as it's only function is to provide you with an ip address.