Usually this happens because there is already a msnmsgr.exe process open in the task manager. To remedy this, open up the task manager by pressing Ctrl-Alt-Del and clicking Task Manager, or Start > Run > taskmgr.
Find all instances of msnmsgr.exe and end those processes, and then reopen the program
This fix is usually applicable to programs other than MSN. In a way it is also a general solution for programs refusing to open.