Seems like your router have lost the port forwarding settings. This could happen through a update on the router by your Internet service provider. that would be as well the reason why it works at home but not some elsewhere. Just think about a kind of firewall (NAT) between the Internet and your computer, installed on your Router.
I would suggest to go on the website portforward.com. There you select your Router and the search for Sling. Try to re setup the port forwarding then it should work again. Furthermore you should search for port forwarding in this forum or on the help articles.
Hope this helps, feedback would be nice.