If this happens after you close IE, then open the Task Manager, then click the Processes tab, look for any entry for "iexplore.exe", highlight, then click the "End Process" button.
See if that allows Desktop icons to work.
Many IE problems can be traced back to bad Add-ons. You can check IE's Add-ons by going to Tools > Manage Add-ons, and disable any that may be causing this.
I use IE8 and Thunderbird with Win 7, and have AVG 9.0 as my anti virus.Using for some time. After using IE8,the desktop shortcuts lock up or freeze. Will not work.I must reboot for everything to work again.