An interesting question.
First, I'd go with his line when he kills Polonius:
Ham. [Drawing.] How now! A rat? Dead, for a ducat, dead! Kills POLONIUS [through the arras].
If he really thinks Polonius is a rat, that's crazy.
Related is this line:
I’ll lug the guts into the neighbour room.
People who drag bodies around casually aren't that balanced.
In between, you can use this one:
Mother, for love of grace,
Lay not that flattering unction to your soul,
That not your trespass, but my madness speaks.
It will but skin and film the ulcerous place,
Whilst rank corruption, mining all within,
This emphasis on his mother's purity seems unbalanced.
And, of course:
Why, look you there! Look, how it steals away!
My father, in his habit as he lived!
(He's seeing ghosts.)