You can't open a shortcut file, because a shortcut isn't really a file. It's just a pointer to the real file.
Think of it like this: you put your keys in your coat pocket, but you're worried that you will forget where you put them. So you put a note on the door that says "Your keys are in your coat pocket". The shortcut is just like the note; it's not what you'r looking for (your keys) but it tells you where they are.
Need more details as to what is going on. Is it not opening whatever the shortcut points to? It could have been moved or deleted then. Do a search on the computer for it. If it's a web link, it could be pointed to the wrong place, or the site no longer is there, or the page has changed.