the current situation is that I just read this morning that Hamachi needs to be placed at the top of the list; I did that, but my friend hasn't tried it yet. My antivirus is Avira; I don't know what my friend's is. I'll clarify and add new information when I know, but for now, please share any information you have on this.

Added 3 minutes later
Also, in the Start menu, the Nival Interactive section doesn't seem to be related to either 1C or Heroes of Might and Magic. Hamachi is working fine for us; we've played some games through it without any problems. I don't rule out the possibility that our version might not be suitable for Heroes of Might and Magic III 3.1, or that some settings might not be activated.