Hey!

Basically I would want to play this game with a buddy of mine over the internet. Is it possible with the complete eddition (not hd) provided in GoG?

Thanks a bunch!

Yes, the game supports direct TCP/IP connections and LAN. (Though for best results in banter and scumbaggery, use hot seat :) )

To use direct TCP/IP connections, the host should know his IP address (which can be easily checked on ip-lookup.net) and tell it to the other player. The other player, who is in the Join Game menu, should only type in that IP address if the room is actually made, otherwise he'll just get a message the IP can't be found.

Of course, this requires Heroes III to be in the exception list in your firewalls. If you get stuck, post back here!

Yes, it is very much possible. I couldn't get the TCP/IP thing to work without a little support from Hamachi though. I found this to be a nice visual guide to work with Hamachi:
http://wiretuts.com/how-to-get-games-work-with-hamachi-on-windows-7/

It's not specifically for HOMM 3, but it helps. Otherwise, one just has to remember to use the internal Hamachi IP you're given, also, firewalls can be problematic.

If you have problems, do ask.