What small section of the text shows Hamlet engaging a question that cannot be answered?
I think that you can find any soliloquy where Hamlet ponders a question that cannot be answered. The "to be or not to be" moment would be one such moment where he brings out issues of existence or of consciousness. Naturally, he is left with no answer. He is left in this condition because of his own nature, to allow function to be smothered by surmise, and because the nature of the questions he raises are, by definition, difficult to answer. Issues of consciousness, good or evil, redemption, and the motivation behind individual actions are complex and ones that are more predisposed to being unanswerable than containing definite and fixed answers.
I think that the clearest example of this comes in his famous "to be or not to be soliloquy. In that speech, he is engaging in a very deep question that can certainly never be answered in any objective way.
In this speech, Hamlet is trying to decide whether life is worth it, basically. He is trying to decide if the evils of life that he does know about are worse than the evils of death, which he does not know about.
It seems to me that no person alive can truly know the answer to these questions.