I'm not sure how to do it, but it should resemble the form of the literature.
Jacques Prevert, French poet of the 1940s and 1950s, did just this by making a word play on the French word for or. For, ou means or, but when there is a grave accent over the u [`] the word o`u means where instead.
So, there is a student who is a daydreamer named Hamlet. When the teacher calls upon him to conjugate the verb to be and Hamlet says, "I am or I am not," "You are, or you are not," the teacher makes the pun, "Yes, Hamlet and you are where you are not," I think. But, Hamlet retorts, "Precisely. And to be where one is not is also the question!"
Perhaps you can make a pun upon some word in Hamlet's speech which then changes much of the meaning without altering the word's spelling, etc.
What about to shave or not to shave-that is the question:
Whether 'tis better in society to squander
The manly privelege of growing hair
Or to suffer the daily task of shaving
and by doing so give credence to societal pressure
Not great, but at least you get an idea.
I like Poster #3's response about action and inaction. If you want to take it up a notch, make the action something that most people would not take and make it seem more desirable than the inaction that most would prefer. That's what Hamlet does with suicide. He makes committing suicide seem more appealing than living. He uses very appealing terms to describe suicide, making it seem the braver thing to do, while living is presented as being painful and horrible. But suicide has a catch, "a rub," that prevents us from "taking arms against a sea of troubles," and that catch is our fear of the unknown in the afterlife. You might do the same with something as mundane as "To skip or not skip school." If you use the above editor's example "To do your homework, or not do your homework," you would make doing your homework seem to be horrible, painful, tedious, something that students "bear," rather than fight. "To not do your homework" would be described as being courageous and noble. But there would have to be catch--grades? college? graduation? Good luck.
The question really is about action versus inaction, so no matter what you decide you have to consider the consequences of the action and the lact of the action. What immediately comes to mind is something like "To do your homework, or not do your homework, that is the question." This actually sounds like a kind of fun assignment -- be creative but follow the structure of the original!
There seem to be two challenges here -- finding a way to parody the speech, and then writing your own text that keeps to the form of the verse, iambic pentameter. I'll start with looking at a couple of ways to approach choosing the theme of a parody, and the give you some tips for working with iambic pentameter.
First, a parody (Enotes definition) is meant to:
mock, comment on, or poke fun at an original work, its subject, author, style, or some other target, by means of humorous, satiric or ironic imitation.
The key to this definition is that you must imitate something about the work -- the subject or style being the two possibilities that jump out at me. The subject of the speech is the question of whether it is preferable to live and suffer the pains life brings, or just end it all, especially the suffering.
So, to parody the subject, you could create a list of ridiculously intense or ridiculously trivial pains of suffering that you'd like to avoid. Then you could consider the act of suicide in a similarly grotesque or bland way. The taking of the subject and completely reducing in or completely blowing it out of proportion would give the satiric irony that a parody requires.
You could also parody the form and take up another question all together. The parody here would come in taking some trivial topic and treating it as the dire question the speech confronts. "To paint my fingernails or not to paint my fingernails/That is the question," for example. Again this could be any topic, but you must carry forth your idea and consider the pros and cons of both sides, just as Hamlet does in the speech.
And finally, iambic pentameter is the verse structure that you should attempt to stick to. The most important think about this verse structure is the rhythm and number of feet per line. Not an especially easy assignment. However, Enotes has a nice, easy to follow description of iambic pentameter and how it works. I've pasted the link to that page, along with one to a definition of parody and an essay about Hamlet's speech.
Good luck with your assignment!