Try using something like http://www.longtailvideo.com/support/jw-player-setup-wizard .
and include it on every page.
Set the current position, (onunload) using javascript to a cookie, then set the start point automatically and start playing it using javascript on the next page. All you need to do is write the javascript to include the player, and put it on every page.
I think you'll have to write it.
Of research for someone who has written it.
But in my short research time, I couldn't find someone who has written something like it.
Personally, I hate websites that play music. If there is not an easy way to turn off the music on the site by clicking a button, I will go to another page that sells or talks about the same thing.