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How about a massive meteroite (size of moon or larger) on its way to the earth. Mankind is able to distract the meteroite, but it hits the venus. As a outcome, chunks and dust, which where venus and meteroit before, are now on the search of a stable orbit around the sun. This blocks (partiell, periodically) sunlight and changes weather dramatically. The exact weather change is not forecastable, so you could actually do what you want in your story.
While nothing in this answer is wrong, it would be worse, by far! Electromagnetism is one of the fundamental interactions. It has a role in how atoms assamble, align, interact and so on. It's reasonable to say that, without electromagnetism, we would collaps or burst instantaneously.
I claim, any meteroite, which we would not be able to fend off in some way, would be so large, it would destroy the entire earth. How about a massive solar flare, burning off our atmosphere?
