Hamlet's Obssession with Death

From the start of the play, we find out that Hamlet is depressed over the death of his father.  He keeps contemplating death throughout all of Act I, and in many ways begins to become obsessed with death.  It isn't until Act I, scene v that Hamlet discovers his father was actually murdered by Claudius and is asked to seek revenge. 

So, why is Hamlet obsessed with death?  While, it may seem that his obsession is a direct result of Hamlet's fathers death, I don't think it is that simple.  Hamlet is clearly well educated, more so then most other characters in the play.  Thus, it would be reasonable to assume that Hamlet likes discovering truths about the world.  When Hamlet's father died, it could be possible that it brought the issue of what happens after die to the forefront of Hamlet's mind.  As a result, it has caused him to question to purpose of the living world as shown in the quote:

How wear, stale, flat, and unprofitable
Seem to me all the uses of this world!
Fie on't! o fie! "tis an unweeded garden
That grows to seed; things rank and gross in nature
(Act I. sc ii.)

To me, this quote shows that Hamlet sees the world as an inevitably decaying world, that everything is going from good and beauty to bad and gross.  Thus, I don't think it was his father's death that put him into a depressed mood, but instead the realization that everything alive is decaying into death that makes him depressed.  Because there is no longer any purpose to living in Hamlet's eyes, Hamlet actually wishes he wasn't born as shown in the quote

O that this too too solid flesh would melt,
Thaw, and resolve itself into a dew!
Or that the Everlasting had not fix'd
His canon 'gainst self-slaughter! O God! O God!
(Act I. sc ii.)

It is clear that Hamlet, seeing no purpose to life, sees life as nothing more than suffering, and as a result wishes he didn't have to go through life anymore because he tired of seeing everything and everyone suffer. 

However, Hamlet soon gets a purpose to live once his father asks him to seek revenge on his murderer Claudius.  As a result, Hamlet begins to move his intellectual thoughts toward the morality of seeking revenge and redemption.  He is still obsessed with death, but it becomes more focused upon the actual events concerning death rather than death itself.  He questions the morality of killing Claudius to seek redemption for Claudius killing his father. 

Thus, it is clear to me that Hamlet's obsession's are as a result of his continuous searching for answers of issues such as death and morality, and not from his sadness over his father's death.