The nice little endy bit of Act Three, blurring in with Act Four.

WELL.
That is more goddamn like it!!
Some death!
This is what I was waiting for.
So Hamlet runs off to his ma's room because she wants to talk to him, maybe hoping that, just maybe, she's realised that Claudius killed her first husband, and so he can tell her what's really going on.
Alas.
She calls Claudius his dad and says that Hamlet has upset him.
I think this probably started making Hamlet a fair bit angry, seeing as how, even after his dramatic efforts, no-one believes him that Claudius killed Hamlet Sr.
Although, to be honest, I'm querying if turning it into a play was the best idea, because now people of the court, thinking that he's gone a bit doo-lally as it is, are just going to tell him "No, dear, that was just a play."  So possibly there's the fact that Hamlet's master plan of wonderfulness is actually a bit rubbish.
And HE STILL HASN'T KILLED CLAUDIUS.
But I digress.
He runs into his mum's room and she goes "Alas, Hamlet, you've gone mental" (not exact words).
Then Hamlet starts mucking about, shoving her around and Polonius, from where he's hidden in her closet, freaks out and shouts for help.
So Hamlet stabs him.
This is actually fairly refreshing after his general pansiness of before.  He's previously been a bit of a weakling, and more of a thinker than a fighter, which, in Shakespeare, is a little bit disappointing.
But NOW he's stabbed his girlfriend's dad.
Wahey, really.
Much more exciting.  Before, there haven't been so many major plot twists.  Sure, espionage and forbidding and all sorts, but no real TWISTS, apart from that  big old "poison in the ear" thing.
So Hamlet has gone even more mental than before, possibly now sincerely mental.
Now it's really getting fascinating, and is becoming more compelling to read onwards and discover what's going to happen next, where before it was all a bit like "Oh, he's going to go mad.  Oh, he's got his bojangles out.  Oh, he's being packed off to England because they want him got rid of."
Now it's getting good.
So, he's killed the dad of his girlfriend.
And now SHE'S going mad.
Madness seems rather prevalent in this play, whether accidental (i.e. brought on by the brutal and unfortunate killing of the character's father) or put on (i.e. oh my God, Uncle Claudius killed my Dad, let's pretend to go mental). 
And so Ophelia, the lovely Ophelia, starts singing all over the place.
And when her brother shows up, trying to steal the throne from Claudius, he declares her insane and now has to grieve the loss of his father, his father's body, and now his sister's sanity.  Not a good day for Laertes.
Not that it won't get worse if he finds out that Hamlet not only stabbed his father to death, sent his sister mad and hid the father's body, but that the body is more than likely chopped into thousands of pieces because Hamlet rather let go of all his control and took his sword to the corpse.
Pretty mad.