There is almost no companies out there that are going to lock down the GUI so far that you can't move icons around on your desktop.. thats just cynical insanity.
There are a lot of reasons for either IE tabs to not be able to tear away, and also if often affects the Desktop icons, in that you cannot move them around....
some of the ones I have run into:
1) Aero causes an issue (especially with dual screens) turn off Aero and see if that solves it.
2) if you recently updated Video drivers, roll back to the previous. if you have not recently updated then try to update to the most recent. I have seen a lot of posts about Nvidia cards specifically having this issue.
3) Select "start" button - click "run" - type "regedit" and hit ok.
in the new opened regedit window , navigate to the below path
delete this entry "no active desktop changes" and restart the machine. (this worked for me)