[MuGen]

Well is IE opening when you go into START > RUN > c:\program files\internet explorer\iexplore.exe

If not theres a huge problem there.
If yes...then theres a problem with your shortcuts. Something might have been changed like a folder name so icons won't load the right program or don't load it at all.

Solution:
Uninstall IE, before installing it again.
After Uninstall, Install IE

See what happens.... but usually if you need to repair something it helps to remove any instances of it, before installing again.