Location of iexplore.exe:
C: \Program Files\Internet Explorer
If after browsing to the above location with Windows Explorer:
My Computer, C: drive > Program Files > Internet Explorer folder, you can run IE OK from here, the shortcut is at fault.
If IE does not start up from here - IE and/or Windows may be damaged. Perhaps a reinstall via
www.microsoft.com/ie may help - or - use Windows System Restore utility to revert to a time when IE was working.
System Restore is located in the Start Menu > All Programs > Accessories > System Tools..
Good Luck!