After installing GOG version game requires CD and lets me play in multiplayer only. I realised that sometime ago I had installed orginal CD version on my PC. Probably there was some registry entry left. Additionally the movie at the beggining of game was not there [the one that shows only once and you can't skip] which confirms my theory about registry leftovers.
I tried it on my secondary PC and i had no CD problem and the intro was there.
anyone knows whats need to be claened from registry?

yes, that solved it:
i found three entries with 'new world' in name [I use vista64]
HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\New World Computing\Heroes of Might and Magic® III\1.0
HKEY_USERS\S-1-5-21-3282000464-2524194729-134016098-1000\Software\Classes\VirtualStore\MACHINE\SOFTWARE\Wow643 2Node\New World Computing\Heroes of Might and Magic® III\1.0
HKEY_USERS\S-1-5-21-3282000464-2524194729-134016098-1000_Classes\VirtualStore\MACHINE\SOFTWARE\Wow6432Node\New World Computing\Heroes of Might and Magic® III\1.0
second and third was old b/c key with name CDletter [or something] was set to 'E:' in first it was 'C:'
i removed all key groups and installed it again. Now the intro was there and i can play camaigns
Thanks

Glad to hear that sorted it, its such an awesome game.

i've just been grappling with this problem when trying to install HOMM3 on my netbook. the error appears whenever i install the game onto an SD card, but it works fine without asking for a CD if i install on the C: drive. i'm glad the game works but it would've been nice to keep it off my tiny 8gb ssd. fallout installs and runs fine from the SD card so i wasn't expecting this kind of issue.

It's not an issue with the GOG version though, but with the original CD version not cleaning up the registry properly on uninstall. Sucks, but not really much they can do about it that I can see...

yeah, though i wiped every entry from the registry (i'm running xp). in any case, i found a workaround: after installing to my c: drive, i copied the program folder to my SD then uninstalled the game. it now runs fine directly off the SD card and doesn't demand the CD.

twilightdragon1's solution worked perfectly for me too, on a netbook with Windows XP Professional 32bit. I didn't need to reinstall anything, just change the value of the registry key he described from D: to C:.
EDIT: I have Windows installed on C:, and the game installed on a SD-card designated D:.

I was having the same problem when trying to install to a USB... went into the
HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\New World Computing\Heroes of Might and Magic® III\1.0
directory and added a string named CDDrive with value C:
works fine now

This guy solved my problem >: P

The pic especially was super helpful.

hey there, im new to this site, just signed up today b/c i LOVE HoMM3C! can you help me get my game to allow me to play multiplayer games? i have the 'CD problem' u described, but that is the only problem with my game. everything works except multiplayer. my email is >shadow77727@msn.com< I would greatly appreciate the help!
hey Bombader, can you help me figure out how to do multiplayer with Heroes? u seem to know more about this registry key stuff than i do. i know more than most about computers, but i only know so much. i would greatly appreciate your help.

I tried the solutions detailed above or rather; I encountered issues with the suggestions. I had HoMM3 - The Shadow of Death installed, but it would constantly crash on this windows 7 laptop. I uninstalled the CDROM version before installing the GOG complete version. And I get a screen that says to play single version games I need to quit and insert the CD and restart, but even with the CD it still gives me the no CDrom error screen. I checked the registry and can find no 3DO or NWC folder, thus I can't make the registry change suggested. And I am not having issues with the startup. What now?

I am also having problems with getting HOMM3C to run. I am having the same CD missing issue as others, but despite deleting the disc version of HOMM3 and all NWO and 3DO files using regedit (to my knowledge, at least), I can't get the game to run in single player. Changing the CDDrive to C: doesn't work because it's already set to C:. Quite perplexed by all this. I'm running Vista Home Premium.

Just download and run Heroes3HD mod, it works completely fine with it. And you can also choose larger resolutions which helps a lot. :)

There is a thread about it:
http://www.gog.com/en/forum/heroes_of_might_and_magic/homm3_hd