If you are trying to play Hearthstone, now in open BETA, and are having a problem where as soon as you hit the Play button the screen or window goes dark and the process in the task manager says it’s “Not Responding”, I may have a fix for you.
I had this very same problem and after no help from the forums or tech support, I figured it out myself. Really it was just basic troubleshooting. Getting to the part that helped me with the problem, I disabled my firewall and associated agents (I am running Avast Internet Security, one of the best), the game suddenly ran fine! Imagine that. That meant that the problem was with my firewall. Sure enough, I re-enabled everything and the game stopped working, went right back to the blank screen.
So, here is where the fix comes in. Even if you aren’t running Avast, this could be your problem regardless of what brand of firewall you are running. Check out what I found and see if you have the same problem with your firewall.
I went into the settings and in the application specific rules section, where firewall rules are associated with specific executable programs, I found rules for the Blizzard Agent, the Updater and many more, even the Hearthstone Setup executable. What I did not find was any rule for the Hearthstone game app at all! They had rules for everything but the game itself! So, I simply added a rule for the Hearthstone executable itself
C:\Program Files(x86)\Heartstone\Hearthstone.exe on my system
and then all went well after that, the game ran fine. The whole problem was that the game executable could not talk through the firewall. Once that was enabled, everyone was happy, including me! I hope that helps you with your problem.