Okay, I have re-read the whole post, and I think that the issues is that you are using the wrong IP Address to connect to your server.
Basicially you should be connecting from the LAN To the LAN IP address of your server. If you go to the exteral IP address of the server (which is actually youw WAN IP address) then you will need to port forward the required ports to the server, and this will prevent multiple PCs from using the same ports as the rules will be created for one or the other (as Colonel Kurtz has found).
The "correct" setup is as follows. (I put correct in Brackets, because this is EECH and things are difficult, and don't always work. However this setup works for me)
Your Server should have a static IP address on your LAN. (Lets call this 192.168.1.4) There should be rules in your modem which forward the required ports 2300-2400 TCP+UDP and 47624 TCP+UDP to the server (192.168.1.4). To get help with this, look up your modem/router on
www.portforward.com and follow their instructions. (Aside from testing purposes, unless your server has a DECENT firewall on it, then you should not DMZ it permanently, this is leaving it open to expliotation from the web, however BammerVB is right in that doing it for tesing is fine, your chances of being attacked in a short period of time is middling to none.)
The server should be set in the eech.ini file to report into
http://hoxdna.org/eech/ so that other people can see your server (if you want internet people to connect to it).
Your local PCs can have static IP adresses or not, this is not so much of an issue
as long as you are connecting to a Server on the LAN.
Start up your EECH and go to Options, Multiplayer and select Internet TCP/IP and delete any IP addresses there.
you should now be able to try combat, campaign, and then -multiplayer- and you should be able to see your server and connect to it. I have only ever got this "automatic" connection to work for servers on the LAN. If your server name does not appear here, then go back to the multi-player settings in eech and put in the LAN IP address of the server, (in this example 192.168.1.4) this should make the connection work.
As long as you make connectiond on the LAN IP address of the server, then multiple PCs should be able to connect to the LAN server fine.
(If there is some firewall software on the server that is "learning connections from incomming PCs that might muck with multiple connections from different PCs. so it might pay to remove/disable it from the server for testing at least).
Hopefully this all makes sense...and helps.
In short, when on a LAN, use the LAN IP address of the server.
(PS, these are for accessing a Server on the LAN, its a slightly different story to access a server on the internet.)
(PPS, If you set up the Port Forwarding rules for 2300-2400 and 47624 to point to a server inside your network (On your LAN) then you will not be able to connect to a EECH server outside your LAN (on the internet) until you change the rules again.)