Well, big problem incoming : i can't play 'cause Windows doesn't find any shortcut for the game. Any ideas of how to fix it ?

Try re-installing the game. If you use the installer's default settings, it'll create a shortcut for the game on the desktop as well as in Window's "Start menu" (usually in a folder named "GOG.com").

If you have got a shortcut and it doesn't work, try right-clicking it and choose "Run as administrator".

Which Hitman (1, 2 or 3) and which Windows version are we talking about?

The first one, not Contracts. And Windows 7.

Which anti-virus are you using? I have Avast(and running Win8.1) and when I tried to run the game with Avast Shields enabled, the "Hitman.exe could not be found" error would be displayed. I'm not sure if this is the problem you're having but I'll post how I fixed it just in case someone that has this problems stumbles upon this thread.

1. Disable Avast Shields and re-install Hitman using GOG installer
2. After installation is complete, close the installer and open Avast go to "Settings -> Active Protection -> Open Settings for File system Shield
3. In File System Shield settings go to "Exclusions" tab and Add an exception for the Gog Games folder on your HDD(C:\GOG Games").
4. Re-enable the Avast Shields then launch the game. It should now launch without displaying an error. I think maybe Avast moves the hitman.exe into quarantine when it is run and that's what's causing the issue.

Hope this helps. Good luck.

Yes, Avast has a false positive on hitman.exe, happened to me yesterday when I finished the download and the setup file got scanned. If the antivirus is configured to take automatic action, it probably removed or quarantined the file (same effect) and you didn't even notice.

The solution above is ok, but it is better to disable automatic actions if you know what you are doing. If you do, you can even report the file as a false positive to Avast's servers and prevent this to happen to more people.

--edit--

One more thing, exclusions should be kept at file level (exclude hitman.exe instead of the GOG folder or even the game's folder). Excluding folders can get tricky and is dangerous in the long run.

After going through the support from Gog, I realized it was Avast. When I tried to install the game, I kept getting a MoveFile failed error. I had to disable avast to install it. Then when I tried to play the game after enabling avast, my game wouldn't start. apparently avast would remove my game.

Is this a problem with Avast or is it a problem with the game?

Submit hitman.exe to Avast.

Do as Gydion says and think about using a different anti-virus software. Compared to others Avast causes too much problems, without doing anything better.

Yes, I did that already. Hopefully it helps. Which do you recommend?

Anti-virus software is almost a religion, so it's difficult to do recommendations. but in my opinion such a software isn't doing a good job when it's causing to much trouble with running common software. Anti-virus software is overrated anyway. Although not the most elaborated search engine, I think e.g. Microsoft Security Essentials is sufficient. It's free, doesn't use a lot of resources and integrates smoothly into the system. But there are others like this. More important than anti-virus software is up-to-date software especially every software connected to the Internet (like browsers, Flash player, messaging software, Java, etc.). When you are cautious opening emails and attachments, outdated software poses the biggest risk for your system to get exploited and every anti-virus software will have a hard time preventing this. So be careful about emails and keep your system up-to-date and you theoretically don't need an anti-virus at all. As long as you don't download tons of programs from unreliable sources. If you've downloaded a file and you want to check it for viruses, upload it to www.virustotal.com, instead of checking it with your local scanner. They're doing a better job.

It's not a problem with Avast. It's a problem with all modern anti-viruses. Even if another won't give you problems with Hitman, it will have problems with something else. In this case it is not a "completely" false positive, the a-v detects a compression tool that is used commonly by malware; even if there is no malware really present.

I found out about the compression tool BS after some research and uploading hitman.exe to http://virusscan.jotti.org/ where I saw that ClamAV detected "PUA.Win32.Packer.Safedisc-1" (potentially unwanted application instead of malware) and not simply informing "generic malware" as other false positives; and then continued researching from there. It's a really bad policy that all a-v fall into at some point.

Scan permalink of hitman.exe: http://virusscan.jotti.org/en/scanresult/1da5e962e92a49f9a5ba2b5a4436083522800fd0/d39d0da1f3b15600e15016b99e7838d62218e9ef

All AV I have used have had the option to add exceptions; I suggest you do just that.

Yes, I am aware of that. I just can't understand why it was never triggered before, because it's not the first time I installed original Hitman and all these years the same firewall software was used.