It seems like there is a bug in the desktop application. When I start the client and there are queues to access the servers (Like now during BlizzCon), the application itself does not load in my desktop yet it appears in the right task bar (Windows).
This means that I cannot navigate the application, but right clicking on the icon allows me to launch games. On the other hand, if I cancel the queue and request to “stay offline” the application loads and then I can join the queues as normal.