HD2 - game is starting and closed immediately

Run HD2 setup (setup.exe, in your HD2 main directory) and turn "vertical synchronization" on. (and fullscreen on) and see what happens.

btw, I will be out of the house soon and not able to respond later today.

you mean to "cut it out" of the file and put it on main file?

I don't understand what you are asking.
Just run setup.exe again in your main folder (like you did before) and enable vertical synchronization and fullscreen to see what happens.

It is strange you have these problems because we all had them on windows 10 when it was just released but windows updates and/or NVidia updates resolved these issues like white borders and game crashes on startup. Are you sure your windows is up to date and also your NVidia drivers?

I would also suggest to install that widescreen solution I linked to earlier, maybe it helps your situation and of course the game is much nicer in 16:9 than in 4:3.

I have still the problem when i enable vertical synchronization and fullscreen, that there are white borders and the game crashes on startup... I really dont know why... My windows and Nvidia updates are up to date... I will try that widescreen solution... Thanks