are you sure your clicking and not dragging the icon? This sounds like the "no-drop" icon you get when you try to drag a program icon over top of another one.
if your sure your not dragging, it could even be a problem with the mouse- a sticky mouse button or something wrong inside that causes the button to stay down; which might explain why you need to perform multiple clicks.
It could also simply be that your "drag" window is too small for you. If your able to determine that the mouse is functioning, I recommend increasing the drag sensitivity value.
First, you need a handy tool from Microsoft, called "tweakUI". It can be found here:
http://download.microsoft.com/download/f/c/a/fca6767b-9ed9-45a6-b352-839afb2a2679/TweakUiPowertoySetup.exeonce installed, It should appear in Start->All Programs->PowerToys for XP->TweakUI. Start it.
Select the "mouse" item, found on the box in the left hand pane. You'll find a "drag" box within the "Mouse sensitivity" Frame, increase this, click apply, and try starting one of your programs that would give you trouble before. Hopefully you will find a value confortable enough so that the computer doesn't mistake one of your double clicks for a drag click
