Sorry, one point of clarification... the orignal web page closes and a new one opens up with the address of the original shortcut placed in it... this is very odd behavior. This is a new HP laptop running Windows 7 ultimate.
Getting same problem on my desktop PC, Win7+IE9. Dragging and dropping onto the desktop works fine from other browsers, just not from IE9. Never had the problem on IE8. However, friends running Win7+IE9 are not having the problem so there's something amiss with my settings somewhere.