Death is everywhere in this Shakespearian play. The deaths of Hamlet, Polonius, Gertrude, Ophelia, Claudius and Laertes --those known as the main characters--all follow the original death that put this play into action--Hamlet's father's death.
Not all of the deaths are meant to happen. There are deaths that are planned in advance. However, Hamlet accidentally kills Polonius--thinking he was Claudius, and Gertrude is accidentally poisoned by Claudius--who meant to kill Hamlet with poisoned wine.
To say this play has a preoccupation with death is an understatement! As for the death of power--that would be a direct result from the greed that the men possess when trying to kill to become king.