Q: Authorize Macbook

What happens when you try to authorise your new computer ?

If you've now reached the 5 computer limit then you should, if you haven't done so within the last 12 months, be able to log into your account and 'deauthorise all' - see the page that you posted from : Deauthorize your computer using iTunes - Apple Support

If you've already 'deauthorised all' within the last 12 months you could try contacting iTunes Support and se if they can/will do it for you : http://www.apple.com/support/itunes/contact/

If it's a different problem that you are having ... ?