Hello there!
I know, i know Bizzard got problems with login servers, but
my problem is maybe different or it’ll help solve the main issue by this.
Login working for me every time, but after that character sreen didn’t show up just two messages:
No servers are currently available (BLZ51934200)
No realms are currently available (WOW51900309)
Hope we can play leeeeroy again soon 
Thanks!
I think their actual server team knows whats going on and has the balls to inform people unlike their official twitter site.
we all get the same message