Oh...
That's easy.
Windows XP theme, by default, has no icons on the desktop except
the Recycle Bin icon. Just reinstall Windows XP and you will get
what I mean.
Whereas in the previous versions of Windows (Windows 9x, ME and
2000), all these icons will be present. In Windows XP, Microsoft
calls this the Classic theme.
That's why when you switched from Classic theme to XP theme, the
icons would disappear and when you switched from XP theme back to
Classic theme, it would appear again.
For XP theme, here's how you bring back the icons.
Right click on your desktop and select Properties. Select the
Desktop tab.
Click on Customize Desktop at the bottom left hand corner.
A new window will open. Select the General tab.
Under Desktop Icons, tick the My Computer box and Internet Explorer
box.
Click OK all the way to apply the settings.
This will put the icons on the desktop again.