I thought that maybe the problem was with the DNS server, but entering the us.battle.net ip address directly didn't help.
Having this problem, I had the great idea to install a VPN, Hotspot Shield. After I installed it, I could access the battle.net site again perfectly. My question is,
Is there a problem for playing WoW or SC2 through a VPN? Like prohibited in the EULA or something like that?