HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

I've started the download. I'll try it out once it's finished. The issue seems to be related to the Windows bitness. My friend encountered the same problem. He installed Windows 7 64-bit for Heroes 7, and he experienced the same issue. Before that, we were both playing through GameRanger.

Added after 16 minutes
Thank you so much! A truly heartfelt and sincere thank you! It works! I mean... it works even better than I hoped!