Even though other games run fine it doesnt mean that it will has well. Some games dont play nice with certain drivers or driver versions, sometimes the game itself has a bug or there is a file on the system it needs, like runtime files or perhaps directx reinstalled.
The hardest part is that the game is crashing without giving any error message at all. It is also possible that it isnt completely crashing so the exe is still running in the background, which would explain the message that the game is already running.
When that happens open task manager and take a look and see if you see anything about the game running. A good way to do that (In case you dont know the name of the exe) is in the task manager go to view and then select columns. In the list scroll down and put a check on "Command Line" and hit ok. Now you will have a new column of the command that was used to start each process and then you can use that to find any that are running from the games folder
First rule when dealing with a crashing game is to make sure you reinstall directx, have the latest sound and video drivers (Both of those will affect the game) and to make sure that any runtime files it needs are installed.
Most games have a redistribute folder in them, and normally the 3rd party files they need are there.
Shane