My network is having major, major issues connecting to Battle.net. The very first time I connect, everything connects fine, but any subsequent connection is guaranteed to fail unless I reboot my router in between connections. Normally this would simply be annoying, but when I try to view the Terms of Use agreement on an account registration page, the connection hangs up and I then need to reboot my router to be able to connect to Battle.net again.
In general, it seems like the applications can't close the sockets they open on Battle.net, but I can't see why this is. I have the same problem with both Starcraft and Warcraft III.
... Well, there's a rather small chance that you're IP banned - it can be pretty freaky. For me, about 10% of the time I was able to connect anyway. For you, it might be different. Sorry, that's all I can contribute.