Today, When I see my desktop it shows my "My Computer" icon like an image above. What is going wrong with my PC?
NOTE: My PC is connected in LAN so, kindly consider that point.
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This is probably not your "My Computer" icon, but your desktop background. If you drag the icon elsewhere, you'll probably notice that the "X" remains in the upper left corner. Try changing your background image.
There might also be something wrong with you Active Desktop settings (assuming you're still using Windows XP). You might want to try disabling this feature.