Many thanks for the kind words, and glad you're enjoying it so well.
Usually with a connection problem like this, when Hamachi is involved, it's a matter of a problem with the ports or a firewall thing. If you've got Windows Firewall on, or any firewalls associated with your antivirus software (you might have one and not even know it, that's pretty common), then you'll want to make sure and add an exception for either AI War, or AI War's port, or both. If you're able to ping through Hamachi that's a great start, that just means the following is remaining:
1. Make sure you're both using the same port with AI War.
2. Make sure you're using the Hamachi IP addresses to connect via, of course.
3. Make sure any firewalls on both ends are allowing the AIWar.exe program and/or its ports.
And that really should do it! With Hamachi, often you need to do the direct connect rather than it finding it directly on the LAN, but that seems to vary by OS and firewall more than by hamachi.
Hope that helps!