The only way I have found so far to put the Internet Explorer icon on the Vista desktop is by way of the Windows Registry. If you would like to have the Internet Explorer icon on your desktop, then follow the instructions detailed below.

Caution: Editing the registry can be very risky. A mistake could result in the re-installation of your operating system. Be sure to make a backup copy prior to making any changes.

1. Go to Start>> Search. Type in: regedit
2. Drill down to the following registry key:
   
   HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\HideDesktopIcons\NewStartPanel
    
3. Single click the NewStartPanel entry to empty its contents in to the right pane.
4. Right click an empty area of the right pane.
5. Copy the following in to the DWORD name text box:
   
   {871C5380-42A0-1069-A2EA-08002B30309D}
    
6. Click OK and then close REGEDIT.
7. Right click an empty area of your desktop and click "Refresh" from the resulting menu options.
8. Internet Explorer should now appear on your desktop.