Well, Hamlet changes throughout the play, so you could argue that there are many turning points, not just one. However, if I had to choose just one, I'd say it is when the king reacts with guilt to the play within a play. Before that time Hamlet had been waffling, trying to figure out what he should do. (Think of the great "To be or not to be" soliloquy.) After that confirmation of Claudius's guilt, however, Hamlet only hesitates to kill Claudius when he is praying—and he does kill Polonius soon thereafter. When he does, he thinks it is Claudius, and he accuses his mother of Claudius's crime, which ups the stakes markedly. After that, Hamlet is sent away—but returns—and things unravel quickly, with a lot of action.