Monarch.ico is the icon graphic file that would typically be found on a desktop and on which you would click to fire up Monarch. In fact that is probably what you are doing?
Assuming that you are running Monarch by clicking on an icon somewhere. Wherever that is right click on the icon and have a look at its properties.
I suspect the chances are that you are seeing the icon as a graphic rather than it representing a short-cut. If the file extension .ico has been associated with the program Monarch.exe then clicking on the file (if it is indeed NOT a shortcut) will mean that the system will try to open it using Monarch instead of running Monarch.
If Monarch Opens and indicates in the blue bar at the top of its window that it has opened the file monarch.ico you will know that this is the cause of your problem.
What you really want is a short-cut to open monarch.exe and perhaps to associate the monarch.ico file with the shortcut as the icon to be displayed.
Does this make any sense?
Are you running a network installation of Monarch?