You're connecting an unmentioned router to your Technicolor CGM4141? If so, yes, the CGM4141 is just a connection to your router. The CGM4141 will only move data from one network (Cox) to another network (Your router). The Bridge only operates at the Data Link layer so it's not concerned with any routing protocols.
If your CGM4141is in Bridge mode, only its LAN Port-1 is active. If your CGM4141is in Bridge mode, it also changes its IP address to 192.168.100.1.
If you don't have Internet service, that'd be a connectivity problem between your client and the unmentioned router. They need to point to the IP of your router. Can you connect a client to a LAN port of your router?