Peer-to-Peer Online Gaming and LAN Gaming not functioning with DPC3848?

I'm not sure if I can find help here, or really what the problem I'm having is, but I do have Teksavvy and have had very, very few complaints over the years I've been with you guys. Good prices, good speeds.

So, here's the issue. About a year ago or so, my modem was upgraded to the Cisco DPC3848 modem/router combination. Haven't had many problems with it, but recently myself and my girlfriend have taken to some new games to play online, all of which use what I understand to be peer-to-peer connections (Civilization 5, Stellaris, etc). As a foreword, server-based games all work fine, zero problems.

But whenever I try to play a P2P game online, I'm not able to. It will fail to connect, fail to find games, or outright crash the games. I've done enough looking around to see that this specific sort of situation seems unique to me, not the games themselves. In an attempt to try something else, we've tried to play games via LAN, but our computers - both connected to the router via ethernet - cannot find each others' games except in rare, strange circumstances (for instance, my PC can see games hosted by her if her firewalls are completely turned off, but she can't see mine under the same circumstances; programs all added to exceptions too, but only when the firewall is off does anything get through).

I've delved into the router's settings, and can't seem to figure anything out. I don't even know if it's the problem, but every tech friend I know is telling me it should work in the various ways I've had it set up with firewalls, etc, but it doesn't.

Is there something I'm not thinking of? Is it just the hardware? As a final note, I never had this problem at the last place I lived, when I had the more standard modem -> dlink router -> computer. These issues have only happened once I switched to the Cisco modem/router combo.