Hamlet is alive

Not only is Hamlet very passive and someone who is not taking action for being hurt as much as he is at this moment. He talks to himself about ceasing his existence.
In class we discussed that it was after he sees the ghost of his father that Hamlet finally decides to take action and vengeance his father's death. This was seen as a negative trait on Hamlet's part, that it is now that he decides to take action. However, he is in a difficult position, what is he supposed to do before learning that his father's death was not honorable? Kill his uncle for marrying his widowed mother? There is nothing that he can do except either accept what happened or finally leave Denmark and move on and become a respectable king.
Now that his dead father appeared he is given motivation, a motivation that Hamlet was lacking from the beginning of the play. Not even Ophelia is able to motivate Hamlet.

In class we were asked to think about how the ghost appeared. Why did she show up in a full armour suit?
It clearly shows that there was a barrier between Hamlet and her father. It seems to me that Hamlet's dad never really had communication with his son and perhaps it is now that they could start that father-son relationship after death. Going along the argument that Hamlet is dead, could his gosht father be a manifestation of his desire to build a relationship with his father?

Now lets take the argument that Hamlet is not dead. Clearly Horatio was able to see the ghost. Horatio was the first one to see the ghost and tell Hamlet. I would think Hamlet as crazy if he was the only who saw the ghost. If Hamlet told Horatio that it was the ghost that nobody has seen made him kill his father, I would think that Hamlet was out of his mind.

As my previous post states, I think that Shakespeare was able to read people very well. The fact that in his play he had Hamlet create a play which showed how his father was killed was brilliant. He wanted to see the reaction of his uncle, how more psychological can Shakespeare get?