In traditional usage, "like" is a preposition that governs nouns and noun phrases, not a conjunction that governs verbs or clauses.
Its function is adjectival, not adverbial.
Hence one does not write, properly, "The story ended like it began," but "The story ended as it began."
If we change the verbs to nouns, "like" is correct: "The story's ending was like its beginning."
Frequently, then, "like" needs to be replaced by the proper conjunction "as" (or "as if") -- e.g.: "Star-crossed lovers, they are -- like [read 'as'] in the play -- sprung from two households, both alike in dignity." -- Alisa Valdes, "Romeo & Juliet," Boston Globe, 17 Oct. 1995, at 59.
Prime offender: the old ad jingle, "Winston tastes good like a cigarette should."
Subprime offender: headline in the Knoxville News Sentinel 11/21/08: Just like Pearl planned on road