I have tried this game on two computers now. First time it runs fine. After I quit, the second time screen goes black and the game crashes immediately.
I do not have ffshow codec installed.
Things I have already tried:
1. Reinstalling.
2. Rebooting.
3. Downloading the installer again.
4. Running in all possible modes on both computers.
5. Running in compatibility modes on both computers.
6. Renaming the AVI folder.
7. Deleting the AVI folder.
What would be the next step to try to get this game to run? I played this game a long time ago and I want to play it again!

One fix I have just discovered was to rename/delete the adjust.kdt file in the root directory.
After that, the game launches, I can see the intro videos but the menu is invisible. Navigating with the keyboard, you can launch a new game or load a game. New game works fine, however loading does not -- it crashes the game again. Also, after starting a new game, it is impossible to save as it just restarts to the beginning.

I'm having the exact same problem. I tried every solution proposed in the other thread, and none worked. The same things happen if I rename adjust.kdt too.

I had the same problem - the game started fine, crashed on the intro video, than would not start again. I thought it saved some custom settings somewhere, but did not find any files with new timestamp in it is directory. So I looked in the registry and removed all keys that were related to Gorky 17 and did not seem to be added by the GOG installer (I believe the offending key was
HKEY_LOCAL_MACHINE/SOFTWARE/Metropolis/G17/rlist, but I am not 100% sure), and after that Gorky 17 started without a problem, and exiting/starting the game was not a problem after that.

Starting from termit's suggestion, which didn't exactly work for me, here is how I finally solved it on my Win XP:
1) Create a new text file called gorky17.bat in the same directory where gorky17.exe resides (probably C:\Program Files\GOG.com\Gorky17).
2) Edit the file, adding the following two lines:
reg delete HKEY_CURRENT_USER\Software\Metropolis\G17\ /f
gorky17.exe
3) Save the file
4) Right click on the start menu shortcut for Gorky 17 (probably Start->Programs->GOG.com->Gorky17->Gorky17) and select Properties
5) Change the target from "[long_path_not_listed_here]\gorky17.exe" to "[long_path_not_listed_here]\gorky17.bat"
6) Click OK
That's it.
What it does:
Every time before running gorky17, the batch file deletes a few registry entries which the game creates whenever it runs (probably some options, so your option changes will not be saved from session to session).
Enjoy.