It does sound like you are running out of data to play back. Youtube can test your connection speed to the servers they use to see if that is the issue.
http/www.youtube.com/my_speed
Also it never hurts to go hitup speedtest.net and see how fast your internet is on that system.
Just to make sure this is clear, you only get this on the internet, if you have a song on the computer it works fine?
What exactly did you do to chance from intranet to internet(Normally you should not have to change much, unless you had a custom IP ect.).
If you have full system specs, it may help.