Doesn't launch with a GTX 980 and Windows 10.

This doesn't help. The problem is incompatibility with the hardware, as the game itself starts, the intro sound plays, but there is no image. I had a similar issue with another old game - I don't remember which one.

Try pressing [Alt]+[Tab] when you hear the sound! If that doesn't help, then we'll try another approach!

Try running the game in 640x480 resolution (right-click on the .exe file - Properties - Compatibility... where there's an option for 256 colors, and below that, there's 640x480!). One of my acquaintances had this issue on Windows 8 or 8.1! Then we removed that mess (Windows 8 or 8.1) and installed Windows 7 on his new laptop! Because besides issues with Heroes 4, there were also problems with Heroes 3 and even Heroes 5!

P.S. And also, try this utility: DxWnd

P.P.S. And if that doesn't help either, then you can try Equilibris