Can Cox modem interfer with email clients?

First, welcome to the forum! Next, do you know what model modem you had before and which one you have now? The settings should be similar for all models in use. One thing you could check is if advanced security is disabled. Pretty sure it is off by default but could have been left on by a previous user. Another thing to try is to turn the gateway's firewall off for a bit to see if that solves the problem.