wahb64, If I understand your post correctly it appears that all of your desktop shortcuts are also in your Quick Launch toolbar. If you want to hide those Quick Launch icons just right click your Taskbar and unlock it then right click the Taskbar again choose Toolbars and uncheck Quick Launch. You can then Lock the Taskbar again.
I have a Toshiba M35X-S309 laptop and running XP
My wife was using my laptop and she did something so that I now have my desktop icons in a single row a long the bottom of the screen. Also next to the arrow (pointing left) for the tray (in the lower right hand corner of the screen) is another arrow (pointing right). Clicking on this arrow will give you my desktop icons in one column on the right side of my screen. How do I get rid of these two extra desktops??