If you want a shortcut on your desktop you should right click and select "Send To"> Desktop(Create a Shortcut) and the icon will be on the DT. You should be able to do this on any program icon.

Now right click on desktop and select "Arrange Icons by" and choose "Align to Grid" and "Show Desktop Icons" don't select the other options. Now you can move the desktop icons around the way you want and they should stay there.

If you want the program icon back that you lost because you dragged it, open explorer and go to "C:\Documents and Settings\All Users\Start Menu\Programs" and drag the icon back into this folder, now it'll be back where it was and no need to reinstall the program.