I am a few hours into the game, and I have been playing off and on for about a week. Heroes 3 had been working fine. But now when I start the game, it does not respond to input from the keyboard or mouse. I have tried unplugging the mouse and replugging it in, restarting my computer, restarting GOG Galaxy and verified the game download. Alt-tab and Alt-F4 both work, but beyond that, nothing. Heroes 3 just plays the intro movie as if I am not pressing anything.

Bypass the issue by using the HD mod: https://sites.google.com/site/heroes3hd/

Thanks, I'll try it!