Can you confirm the icon is valid i.e. it is showing the icon for your default browser.
Double check that Internet Shortcut is registered correctly, open (file) explorer and go to Tools > folder options > File types > scroll down to URL and ensure it Opens with "Shell Doc Objects and Control Library"
Then check under advanced > highlight open > edit and check that the Application used to perform action: is as follows:
rundll32.exe shdocvw.dll,OpenURL %l
If this is not the case to re-register open a command prompt and type (without the quotes)
"assoc .url=InternetShortcut" hit enter AND:
"ftype internetshortcut=rundll32.exe shdocvw.dll,OpenURL %l" hit enter