To your first question, the complaint of AI War about the port already being in use has nothing to do with your computer -- that's referring to your laptop itself. So, that means that another program is running and using that port; windows (like any sensible OS) only allows a single program to be a server on any given port.
A port conflict like that can only mean one thing: some other program on your laptop is running under the same port. I'm not aware of any other programs that use the AI War port, but it's of course quite possible. That same behavior would also occur if you still had a second copy of AI War resident in memory with that port open as a server.
Regarding not being able to connect to the other computer "because you have the same IP," that's definitely not the case. Your desktop and laptop have different local IPs, even if they do share the same public IP. Otherwise windows would be complaining of "IP address conflicts" and nothing would work in terms of networking for one or both of the machines.
AI War doesn't use TCP any longer (hasn't since last August), so as long as UDP can be reached, that's fine. If you're trying to host a local game of AI War, between your desktop and laptop, you need to be using your local IP addresses. If you're trying to play with the laptop over the internet, and you used to be playing with your desktop, odds are that your port forwarding is still pointing to your desktop instead of your laptop. It can only point to one or the other, though you can change it back and forth as you wish.
If Tidalis is having a "start server error" that's also very odd. It could mean that something else is actively blocking any new applications from being a server (I'd check your security software), or it could mean that something is wrong with the network setup for your laptop in general. No two computers should ever have the same local IP, and the only reason that having the same public IP works is because of the NAT on the router. But if you're playing local-to-local, then your NAT and public IP would never even be used. For that matter, Hamachi also won't work for local-to-local play. You'd just use your local IP addresses, which you can find via typing "cmd" at the help/search prompt in windows, then by typing "ipconfig /all" on the machine to find out what your local area connect ip address is.
All that stuff for Internet play, including public IP addresses, VPN software, etc, all flies out the window when you play locally: you don't need any of it, and most of it just can't even work (because you only have one public IP). And really, you don't want it to work: Hamachi is just simulating a private local network over the Internet. When you're already on a private local network behind your router, you don't then need to simulate a private local network over the Internet back to your existing same private local network that both of your machines are on.
It's really confusing stuff, I know -- hope that helps clear some of it up, at least!
