My copy of Windows 7 was an upgrade from Vista, so looks a little different. I certainly do not have the Desktop button (which I use the whole time) next to my start button, so it must be possible to change it. Unfortunately I do not have a computer with Native Win 7 to give complete instructions.
Pointing at the taskbar, right click and make sure that "Lock the taskbar" is not ticked.
(if it is click on Lock the task bar)
Point at the desktop icon, right click and see if either "Unpin this Icon" or delete are available.
If not then there should be some sliders (thin grey lines) to the left of each section of your task bar, try moving the sliders, to move the desktop ican further away.
Point at the desktop icon, hold down you left mouse button and drag it along the taskbar and see if that repositions it. (this may only be temporary).