The problem with botf like with most other games is, that it expects connected players to listen on specific ports and cause these ports are the same for both instances of the game running on the two different computers, there is a conflict when both computers try sending each other adressing the router which can only forward in one direction.
Luckily your router also establishes an internal LAN with all connected computers having a seperate internal LAN-IP that can be used to address each other within that LAN. A LAN also provides the ability to flood all connected computers for announcements, like botf telling everyone "I'm running and searching for active games" without specifying an ip, like ruthless mentioned. (think about what happened if that would be allowed in WAN, Wide Area Network, the whole internet would collapse!
)However, connecting through warzone wouldn't work, cause it could only tell the internet ip of your router. It tells that ip back to botf when trying to connect, probably using different ports that get triggered through your router for seperating both players of the two computers behind the single router. Both botf instances now try to send to the router ip they got told, resulting in the conflict that the router doesn't know who's meant when both state same ports. Similar problem when using bypass, cause for warzone this just means repeating what it got sent to but again using same old ports and same router ip that's in use by both botf instances. It's NOT mapping the botf ports to the ones players have when joining the lobby and lateron mapping them back to the botf ports. Bypass in this case only means you don't connect each other directly which is often troublesome cause routers block incoming connections they didn't invoke and so didn't expect themselves and one has to listen first (disregarding the NAT punch through).
With Hamachi it should be different, cause Hamachi already catches the packages on your computer before sending them out and then uses it's own ports that you can specify manually if necessary.
When you only want to play with those two computers locally, just use normal LAN, either by not entering the ip for using the flooding technique, or looking up your internal lan ips and using them. So far you already got muzzer2uk, now your problem is a connection error that either is caused by a firewall partially blocking trek.exe or dplaysvr.exe, most probably a software firewall, maybe the windows firewall often people forget, or it's a different version or corrupt installation of botf.
I wish you good success in solving it and hope I've clarified a bit also for others.
