It has happened the same to me everyday during this week, when there is no queue and I try it 100 times, if I get lucky I am able to play so it is even more frustrating because I see it is not even a consistent error…
Yesterday I tried a solution which was to remove the cache folders “Battle.net” and “Blizzard Entertainment” from C\Program Data\ and it seemed to had solved the issue since I was able to play just after removing them (there was no queue a that moment). Today it doesn’t seem to work (There is queue today). You can try and let us know if it works for you.
Here is the post where I saw the suggested solution by one of the forum moderators.