This "C:\Program Files\Internet Explorer\iexplore.exe" is the normal path to the IE executable. Right click on it and make a new shortcut for your desktop. If this doesn't work you may need to re-install IE.
People have already posted it, but this is the proper way I get it done here when it happened to one of our staff members. First we run malwarebytes anti malware, second we run spybot search and destroy, then finally we run the .exe file association fix for the registry. If youre confused by anything here just google!