create empty files:
<game folder>\data\h3ab_ahd.snd
<game folder>\data\h3ab_ahd.vid
<game folder>\data\h3ab_bmp.lod
<game folder>\data\h3ab_spr.lod
<game folder>\h3blade.exe
or choose "Other(Default)" in the "Your HoMM3 Version" field in the Heroes3HDSetup.exe utility
I couldn't find the option to select the game version; I created the empty files, and it started working. BUT:
The quick army management ([CTRL]+click, etc.) doesn't work in the hero and city windows. But it does work in the information window in the bottom right corner.
UPDATE
I solved the problem by updating the exe file to version 3.2.