I see what you are doing!
When you first come to the board, if you look up at the top next to your avatar, you will see a link that says "show unread posts since last visit". If you click on that, it brings a page up with only the threads that have posts you haven't read since last time you were here. On that page is where you will find the "new" button that takes you to the first unread post in the thread.
Did that make sense to you?