This may not answer your question completely, but that screen can be reached when an app crashes your phone. The part about it not being able to turn on is a little more unsettling. If you're willing to go out on a limb, you could open up the back of the case and remove-reconnect the battery.
If it doesn't boot after this, you may have to do some serious hardware debugging. Generally if your phone can't even get into recovery mode, it's a bad sign.