I found the problem eventually. Ever since Windows 3.1, I've arranged my program groups in a certain way. And ever since they came into existence, I've always moved all Administrative Tools to my personal Start Menu only. Because compmgmt.msc worked for me, I reasoned that the OS is probably tying into an existing shortcut for this menu item. So I recreated Administrative Tools folder under C:ProgramDataMicrosoftWindowsStart MenuProgramsAdministrative Tools and copied the shortcut to Computer Management there again. Sure enough, works just fine now. In fact, if you do this and then remove the shortcut and try to launch from the Start Menu again, you get this error dialog: "Windows cannot find 'C:ProgramDataMicrosoftWindowsStart MenuProgramsAdministrative ToolsComputer Management.lnk'. Make sure you typed the name correctly, and then try again.' (Now if this error message came up even if the folder is gone (which it doesn't) it would have really helped figure this out....)
A good fix for this within the code base would be to point the menu to the actual MSC file instead of to the LNK file....
Not sure this is the same underlying cause for your problem, but you might give it a try.