I recommend going into network settings area for each of your systems network cards and telling the system (network cards memory) to "FORGET" the network and then reboot each respective system. In fact, if it were me, I would do each of the systems while the others were off. In other words, beginning with ALL but one of them off, following the steps above, then turn another one on and follow the same procedure until you do it to all of them. To save time and to see if it works though, test it out on the first system you do it on before you go through it all on all of them. This is the procedure that I use every single time I have to change my router. This is the easiest way to prevent problems while retaining your SSID information (information you're probably already used to and possibly have written down for future use). Even if you don't want to retain this, it is still the best way (IMHO) of preventing problems when it becomes necessary to switch routers, as it clears all of your NIC's caches.
ADDITION: I forgot to mention here that I've been able to successfully ping using computer names, although I normally don't do that, I usually use the LAN side IP addresses - 192.168.0.252 ... etc. I did not "intentionally" change any router settings to accomplish this, so if there is a need for that, then I totally stumbled onto it without even realizing it.