I've tried to run the game, yet all I get is a black screen and only way to get rid of it is to restart the computer.

I am running Win XP, changing compatibility setting didn't help.

I am experiencing the same thing, but on Windows 7.

Do you guys start with the start menu link the game created or with the kkndgame.exe file in the install folder? I think it needs the gogwrapper to run, which is started along with the game in the Start menu link. Also, if you've added the game to your Steam library I noticed that Steam imports the link incorrectly (and Valve seem to have "fixed" the workaround for that issue), making it start gogwrapper without launching the game.
The only issue I've seen so far is that the game crashes to desktop when I push the Multiplayer button, but they also say quite clearly on the game page that multiplayer doesn't work, I'd just have thought they would have disabled the multiplayer feature a bit more gracefully.

I've launched the game from the desktop icon. After I come back from work, I'll try launching it from the start menu.

So, I managed to run the game. The June 2010 DirectX runtime package from the Common troubleshooting steps has helped me.

Running the DX runtime above fixed it for me also. :D

Edit: Actually turns out my Firewall Comodo was the cause, putting it on Game mode stopped it from interfering/stopping the game from running and thus getting the black screen you can't get out of.

I can't get it to work. I'm using XP.

I too use Comodo, however I don't believe that it was the issue. I have launched the game after the instalation of the runtime package and two firewall messages about kknd trying to access something popped up, I have just accepted them and all was fine. Before the runtime package, firewall didn't ask me anything.

Hmm, mine might be failing to ask then..

Edit: Confirmed after added trusted files to defense + in Comodo it now works without the need to set to Game mode. Seems it was preventing game files from accessing others.

I had the Crash to Desktop at Start problem when I launched it from the Desktop .KKND icon.
But when I launched it from the Start Menu icon I got a black sceen, then I got message from my Firewall. the one that comes with Windows XP...that the firewall had blocked aspects of the program.I then clicked the "unblock" button on the message and the game started, no problem.
I then tried the Desktop Icon, and the game started perfectly.
I ain't no programmer, but somethng tells me that a lot of the CTD issues is due to GOG not doing a good job of disabling the multi player program.
It DOES take a long time to load though..about 30 seconds of black screen before the game starts.

Kinda get that vibe too, I don't get any startup issues like you mention, but the game flat out crashes when you pick the multiplayer option in the menu. You'd think they may have had better ways to disable that feature. I only got the long load time the first time I started the game, all other times have been instant.

I can run the game no problem, but my mouse input would lag like hell.

The only way to fix that is to run KKNDgame, but then, the colors would freak out, splashing red all over.

I too, had the black screen when I first started the game, and the first time I played it it had crappy graphics, but when I finished the game I saw a message from Microsoft Security essentials asking if I would allow the game to run. I ticked yes, and since then I haven't had a problem.

Well, I can run it for a bit, but then it starts crashing on me if I try to save, or sometimes it won't start at all, and I have to reboot the PC again. I installed the Direct X runtime, and set the compatibility to Win 95, but it still won't work properly. =/