collo53: hope this will help
Ok, I'll try to help, even though I don't have Windows.
Firstly: it looks like you have renamed "moh_breakthrough" to "moh_breakthrough.exe". If I'm correct, please revert the change to "moh_breakthrough".
Secondly: can you tell me what does the console you have mentioned in the first post say when you try to start the game?
Edit:
For the sake of speeding things ups: the most likely issue, that's often asked about and mentioned on GOG MoHAA subforum as well as on PC Gaming Wiki, would be a problem with OpenGL.
The suggested solution is to copy "opengl32.dll" file to the main game folder (so it is in the same catalogue as MOHAA, moh_breakthrough, moh_spearhead).
How to get opengl32.dll:
I'll
link to the same resource PC Gaming Wiki provided. It's a compressed file called gldirect5_opensource.zip containing several files, one of which is the file we need.
After you've downloaded gldirect5_opensource.zip you have to open it. I assume it simply requires double clicking on it. If not, you can right click with your mouse on that file and use option to extract its contents. Inside should be a folder called "gldirect5" in which is folder "bin" an in there "release" (you should be able to open each of them by double clicking on them). It contains opengl32.dll.
Once you've found the opengl32.dll file, you have to copy it to your Medal of Honor game folder (the same you have on your screenshot). The simplest way would be to drag and drop the file from one window to another (while holding your left mouse button and moving the file with it), or you could use right click menu to copy it, and then again right click menu to paste in MoHAA folder.
And that's basically it. Try to start the game and if the problem was with opengl it should hopefully work.