Single page anchor navigation doesn't work

Question

I have some trouble with the following code. It will work in JSFiddle correctly, but in all of my browsers, it works terribly. It was working correctly. I haven't change anything in the code, and today it's totally not working great.

This is my JSFIDDLE: http://jsfiddle.net/E773g/13/

The navigation function should have the following tasks:

1. Go to the right section that is clicked on in the navigation bar.
2. Update the current class to the current item, also on scroll.
3. When the user is not on the homepage but on a single page with the same navigation, only added index.html#video to the navigation on the single.html, it should go to that section too, that links to the homepage.
4. When the user refreshes the page, the hash should me removed in the URL bar.
5. Minus the header that has a fixed position.