New cable Model Motorola

Just a general question 

If I get a new modem MB8600 by Motorola  and after the initial setup and Cox verified everything is good to go. And I still have no internet, Will I be able to plug in the 

old modem and use it without having to call Cox and tell them that my modem has changed back ?

I changed routers this weekend and after Cox told me I am good to go and that my problems lie with my new Router, I changed back to my old router and everything worked fine without me telling cox that I made the change back.

I am still waiting for the manufacturer to come back with answers as to why my new modem is not working, but thought it was funny that the old modem fired back up.

I also changed to the gigablast speed and was was convinced that the old router would not work with that service. 

Can you help with this questions 

DT