The sentences that begin with a participial phrase are:
- "While in the apple barrel, Jim eavesdropped on the men."
- "Using his wooden leg, Long John Silver walked onto the island."
Therefore, the correct answer to your question is that both of the first two sentences contain participial phrases at the beginning. The option "All answers are correct" implies that every sentence in the provided choices meets the criterion, which it does not.
So, to clarify, the sentences containing participial phrases are the first two.