what turning point, or crisis, occurs in act III

I would say Hamlet confronting the queen and stabbing Polonius would be the turning point. There is no going back for Hamlet now; he is comitted to his revenge against the Claudius. Let me know if you need more.

When Hamlet stabs Polonius through the arras in Act III, scene iv, he commits himself to overtly violent action and brings himself into unavoidable conflict with the king. Another possible climax comes at the end of Act IV, scene iv, when Hamlet resolves to commit himself fully to violent revenge.

i kinda need a lil more and maybe some quotes that connect to this as well...Thank You

Hamlet's tormenting his mother over her relationship with Claudius, and perhaps the fact that he couldn't score with her first,

Come, come, and sit you down; you shall not budge;

You go not till I set you up a glass

Where you may see the inmost part of you.

When Gertrude is sufficiently creeped out and scared she calls for help. Polonius is being way too obvious behind the curtain and Hamlet stabs him. The thing here is that Hamlet thinks it is the King,

Nay, I know not:

Is it the king?

THis is a huge turning point because Hamlet is finally doing something, old school! Hamlet is finally being a man of action even though he killed the wrong guy. Hamlet can't turn back now that he has drawn blood!

the turning point because hamlet follows the classical model made by Aristotle would be when he decides not to kill Claudius because he shows his tragic flaw its an emotional high point when he draws his sword and fits into the description of being a turning point unlike when he killed Polonius but no tragic flaw was present in the whole scene