A much larger problem is likely going to be that the box you purchased is only a modem and the box you rent is a modem/router.
You will have no wifi and only be able to hook a single pc to the internet.
If you have another router then it will work.
Pretty much your only option is to cancel the phone service from charter and go to some form of VoIP service. You will need some kind of adapter to convert analog phone to VoIP. The one you used to hear a lot about is magic jack but there are many such devices. You will then need to sign up with a service on the internet to use this.
Most people including me have just opted to use only cell phones and not pay for any form of land line.