Why does the speaker ask for divine inspiration?
Milton was harkening back to a long tradition of epics when he wrote Paradise Lost. In order for a poem to be an epic, it must contain most of the traits of an epic. The one you are asking about is called "the invocation of the Muse." The narrator of Paradise Lost requests divine inspiration by saying, "I ... invoke thy aid to my adventurous song, / That with no middle flight intends to soar / Above the Aonian mount, while it pursues / Things unattempted yet in prose or rhyme." What he means is, "I need your help to fly, not to the middle hights of grandeur, but to the highest, because the story I'm about to relate has never been told in rhymed or unrhymed form before." It is important that the narrator of the epic poem humble himself to the muse before he begins, since the muses are the nine Greek goddesses of the arts, and are thus better equipped to tell any heroic tale than a human poet.
He asks for divine inspiration because the words he is about to say are complex and delicate at the same time, since they have to do with the fall of man. So, if he does that he needs the right and correct words to express his emotions in the most exemplifying manner that would lead to the world to understand his story.
More on that here: http://www.ajdrake.com/e211_sum_03/materials/guides/ecw_milton_interp.htm