Hello guys, I had the same issue: an error message that says that the servers aren't available. No error code or anyhting, just that message. The game worked for me in the beginning, but I had been playing with my network settings lately. I found out that when I have my adapter settings/ or router on a static ip the game does not work, and so I get this error (while normal internetting does work on a static ip). So when it is on dynamic ip the game works fine!! And having the port forwarded makes no difference for me, it might slightly boost the network experience tho. I hope this is a solution for you too!

Do you have UPnP enabled at the router? Have you tried launching Battle.net as Adminisrtator, then launching the game? Does that make a difference? On release day I couldn't get in until I did an initial launch as administrator. While it's not something I typically do, or approve of, if you run it once as administrator it should force the creation of firewall rules on your local system.

Can you give us any more information? This would include how far you get before you run into an error (example- I can launch the game, can select a character but cannot go further) as well as any error codes you get from the game or the battle.net launcher. To ensure your game is up to date, 1. check for updates using the battle.net launcher then 2. scan and repair files using the launcher again. Thanks!