What an insightful question!
The dead king in Shakespeare's Hamlet, is Hamlet's father, Old Hamlet. (This is the Ghost; he appears repeatedly, urging Hamlet to avenge his murder by Claudius.)
The unresolved hierarchy refers to the Elizabethan's belief in the Chain of Being. This was something that placed all things on earth in a specific order, like a caste system. God was at the top, then probably angels, and then the King, followed thereafter by other nobles, commoners, peasants, and even inanimate objects. The rose is at the top of its chain, the lion is at the op of its chain, and gold is above all other metals.
When a king was murdered (as is the case with Old Hamlet, and even Duncan in Macbeth) there was a disruption to the order of the universe. This caused strange things to occur. In Hamlet, the Ghost appears. In Macbeth, there are earthquakes, an eclipse, and unusual behavior within the animal kingdom.
The Elizabethans believed that order would not be restored until the rightful king was on the throne, as God ordained who should be king. In essence, it was a sin against God for a human to remove a king from the throne: only God could do this. (This idea still existed in the time of King George who saw himself as a monarch by "divine right," ordained by God.