I recently purchased a copy of Age of Empires 3 but I have been unable to get it to connect to my friend's game via Tunngle or Hamachi. The strange thing is that I am able to see his game, but when I click join nothing happens. There are no errors or anything so I have nothing to go by. However, my friend can't see a game I host. I've spent hours trying to get this going and am fed up. I experience the exact same problem with Age of Mythology.
If it is a legal copy, then the only reason I can think off is a router / firewall problem.
First, you have to check what port AoE III / AoM runs on, once you found this port you have to forward the port on your router.
I looked up the ports of AoE III / AoM for you, and came up with: AoE III: port 2300-2310 on both TCP and UDP. AoM: port 28800-28805 on TCP and 2300-2400, 6073 on UDP.
To forward the port you can pick the router you are using from the list here and then follow the guide.
If it still didnt work correctly, we got to check the firewall
This link has a great way of learning you how to (un)block a program for your firewall. Make sure AoE III / AoM isn't blocked!