Explanation:

- Option 1: Scarcely she had

- The correct structure for this sentence is "Scarcely had she heard the news." The error is with the placement of "had" and "she," which needs to be inverted after "scarcely."

- Option 2: she fainted

- This part of the sentence is grammatically correct. It follows the correct sequence of tenses.

- Option 3: heard the news

- This phrase is grammatically correct and doesn't contain any errors.

- Option 4: when

- "When" properly links the two clauses and is correctly used in this context.