ok,
You dont use user profiles on your machine do you?? As this would explain why you cant do many of these thing. If you are networked can you log on ok at another machine as you, or as another user on your machine??
Can you right click on your desktop, and select properties to change the desktop settings.
On your desktop how are the icons arranged, (Auto Arrange), this would explain not being able to move the icons, but I expect the icons and darg and drop are part of the same problem.
How do you cut and paste crtl+v / ctrl + c or right click and cut??