Thought I'd share this for others having the same problem, even though the solution is already available in the forums - I just had a hard time finding it, and maybe this will make it easier for others.

Setup:
Intel Core i7 920 (quad, HT disabled), 12 GiB RAM, Vista Business 64bit, NVIDIA GeForce GTX 275 (main and secondary monitor) and 7800 GTX (third monitor).

Problem description:
Running any of the chapters will go through the testing screen (rotating globe), play the 3DO video successfully (sound a bit out of sync, I think), start playing the New World Computing video but hanging after about one second or less (audio sample repeating).

I tried installing it on a laptop (Intel Core Duo T7300) running Vista 32, and that works fine, as do HOMM3 on the desktop.

I've tried all the compatibility settings, running as admin, changing resolution to 800x600x16, making sure FFDShow stuff doesn't interfere etc, to no avail. Editing the registry to skip intro vids helped a little, but it still crashed right before the campaign intro.

Solution:
Heroes Chronicles doesn't seem to work with multiple cores on Vista 64, so change executable (Warlords.exe etc) with imagecfg as described here: http://www.robpol86.com/index.php/ImageCFG (I used both -u and -a switches)

Maybe GoG could do this to the 8 executables and re-pack the installer? Shouldn't hurt to have the executables running on only one core, even if not all systems are affected by this problem.

Nice find! Thanks for sharing.
GOG hardly scans these game-specific forums so there is little chance they will take notice of this fix by reading your post. You could try submitting the solution trough the support section.