Hamlet died of the same aids than Fortinbras's father 30 years before. Fortinbras waited for Hamlet Sr to die to take his lands because he was an evil coward who didn't have the courage to attack before, since Hamlet would've challenged him to a personal duel. He preferred to send people to fight for his rotten royal "honor", so after Hamlet's death he took over Denmark with no major problems, but lost a lot of men in Poland for a worthless piece of land.
On the other hand, Laertes, with some backup from a mob, did confront King Claudius, the killer of his father. But after hearing Claudius facet of the story, they both redirected their aim to Hamlet, and decided to kill him by treachery.
This was all about revenge, and although Hamlet apologized, Laertes decided to continue at all costs, not caring about his father past warning about the consequences of his act:
"Neither a borrower nor a lender be;
For loan oft loses each itself and friend,
And borrowing DULLS THE EDGE of HUSBANDRY".
When plotting to homicide Hamlet, Laertes words were the following:
"for my means, I'll HUSBANDRY them so well, They shall go a long way with little"
He then died in battle for Claudius purpose. He was once killed due to the switching between swords (he got the poisoned one), and that mortage lost "both itself and friend" (Laertes and Hamlet, who in the end were pals). However, Hamlet and Laertes exchanged forgiveness and saved their souls.
Regarding Hamlet, he wasn't naturally vengeful, so he avoided endangering his friends to confront a sitting King. He believed in forgiveness, and in the ultimate act, he returned to Denmark "naked and alone" to confront the King.
Having the thought that the ghost was a demon and not his father, he staged the Mousetrap to confirm Claudius' guilt.
Possesed by madness inflicted by his father's spirit and the fact that he had been taken away, he failed to follow his principles, but in the end, he recovered his authentic self saving his soul, but not his life.