Well, it sounds more like a Windows error than a User error. It could be if you have some application installed on Windows that manages the Taskbar, Start Menu, or some other aspect of Windows, that software is interfering with the icon on the Taskbar.
How do you launch MC? From an icon on the Taskbar? That's what I do. I've never seen what you are describing, and I use an icon on the Taskbar to launch it. When I close MC and leave the Media Server running, the icon on the Taskbar changes functionality, no longer showing a preview of MC when I hover over it, but showing the link to launch MC and the "Unpin from taskbar" option.
If you do have an icon on the Taskbar to launch MC, then I suggest that you unpin it from there and launch MC using the Start Menu or an icon on the Desktop. Reboot after removing the Taskbar icon. If the problem persists, inspect the properties of the icon/shortcut you are using to launch MC and see if there is something strange about it.
It sort of sounds like the icon on the Taskbar actually represents the Media Server, and not MC itself. That could happen if the icon/shortcut you are using to launch MC has a command-line switch to start Media Server, such as "/MediaServer".