Ifty -
Clear your cache (delete files + offline content), cookies. Reset your web settings.
Run HijackThis, and post it here.
I somehow doubt this is the case, but make sure:
Tools->Internet Options-> Advanced tab - Make sure the checkbox "Reuse windows for launching shortcuts" is not checked.
As American Zombie mentioned, IEFix is a valuable tool.
It should clean it up well for you. If it doesn't work, there are a few ways to proceed from there - you could reinstall IE6 (yes, you can on XP)
If you go into the Task Manager - take a gander at the process tab - is there only one instance of iexplore.exe in there? When you open another one, do you notice that there are briefly two instances?