Well, the application isn't called internet explorer.exe for a start - it's actually iexplore.exe. Also, the correct file path should be c:\program files (x86)\Internet Explorer\iexplore.exe
So, whatever virus you had, it's hijacked your shortcuts and networking system to point towards that fake application (more than likely part of the virus).
Go into My Computer and go down the folders as listed above and see what's there are not - you can't actually get rid of Internet Explorer.
Give your system a good clean out using anti virus like Avast, Avira or even Microsoft Security Essentials and see what happens. Malwarebytes is also a great scumware killer.
If nothing still, you could try downloading Internet Explorer from Microsoft and doing a re-install, unless Windows Update catches it and tries to do an update/re-install itself.
But, IE isn't the best browser so you could try something else like Firefox or Chrome.