Whether I try the HD mod or the original EXE, the intro just doesn't display. Tried the registry and everything.

In the HD mod, it's probably intentional (since one issue of the original was the unskippable/repeated intro if the registry wasn't correctly updated)

Using the original EXE however works for me; i have a H3 Complete installation with the HD Mod, and if i manually launch "Heroes3.exe" from the main folder, it does play the logo movies and the cinematic videos as usual