Do not itself unkennel in one speech,

It is a damnèd ghost that we have seen,

And my imaginations are as foul

As Vulcan’s stithy."
 
Vulcan: God of fire in Ancient Roman mythology that was often depicted as a blacksmith. A "stithy" is defined as an archaic object that is used to forged metal. Hamlet is saying that if Claudius shows no signs of guilt within one speech of the play, then he was crazy for thinking that Claudius could have committed such a crime.

"'Tis now the very witching time of night,

When churchyards yawn and hell itself breathes out

Contagion to this world. Now could I drink hot blood

And do such bitter business as the bitter day

Would quake to look on. Soft, now to my mother.—

O heart, lose not thy nature, let not ever

The soul of Nero enter this firm bosom.

Let me be cruel, not unnatural.

I will speak daggers to her but use none.

My tongue and soul in this be hypocrites.

How in my words somever she be shent,

To give them seals never, my soul, consent!"

Nero: A tyrannical Roman emperor from 54-68 AD that was known for his cruelty. He was famous for capturing and burning Christians in his garden at night to provide a source of light.  Hamlet is saying that he wants to be cruel like Nero and evoke an emotional response in his mother, but he doesn't want to harm her or become a monster. 

"Oh, my offence is rank. It smells to heaven.

It hath the primal eldest curse upon ’t,

A brother’s murder. Pray can I not.

Though inclination be as sharp as will,

My stronger guilt defeats my strong intent,

And, like a man to double business bound,

I stand in pause where I shall first begin,

And both neglect. What if this cursèd hand

Were thicker than itself with brother’s blood

Mark of Cain: The story of Cain and Abel is found in Genesis Ch. 4, Cain killed his brother Abel out of jealousy and was cursed with a mark by God. As Claudius sits in his room reflecting on his actions, he is asking how he can be forgiven when he has done something that is so frowned upon in the bible. 

"Look here upon this picture and on this,

The counterfeit presentment of two brothers.

See, what a grace was seated on this brow?

Hyperion’s curls, the front of Jove himself,

An eye like Mars to threaten and command,

A station like the herald Mercury

New-lighted on a heaven-kissing hill"

Hamlet is comparing each characteristic of his father to one of these powerful Gods, in order to show his mother how much superior his father was to Claudius. By giving his father all of these godly attributes, he is making Claudius seem weak and useless.