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She did not buy the cell phone because her sister had one.
Does the sentence has the following three interpretations?
She did not buy the cell phone because her sister had one.
We do not know whether she actually bought the phone. There are two possibilities: she bought it, or she did not buy it.
If she bought it, the sentence only makes sense if we interpret is as statement that the mentioned reason was not the reason for the action:
She bought the phone, but not because her sister has one. (your sentence 1)
If she did not buy the phone, the sentence makes sense as a statement that the mentioned reason was the reason for not buying the phone:
Because her sister has one, she did not buy the phone. (your sentence 3)
Your sentence 2 (She didn't buy the cell phone not because her sister had one) seems to have an extra negation in it. She did not buy the phone and the reason was not that her sister had one. Apart from this logic making my head hurt, I think that since the original sentence has one negation, you cannot just add another one without changing the meaning.
It is very interesting to see that the sentence as you put it can be interpreted in two very different ways. If we do not know whether "she did not buy the phone" is true, we do not know what the second part means.
Basically, if we interpret it as your sentence 1 (she bought the phone for other reasons than her sister having one), we apply the not to because, instead of the verb buy.
We can, interestingly, not do this if we change the order of the clauses:
Because her sister had one, she did not buy the cell phone.
This is the same sentence as your original, just in a slightly different order, and now we know she did not buy the cell phone. We can no longer read your sentence 1 into it, we can no longer link not to because!
