💡 Detailed Explanation
The compound verb ending '〜し始める' (shihajimeru - to start/begin doing something) is attached to the stem form of action/change verbs. Option 4 is correct: 'Since it started raining, I hurriedly opened my umbrella.' Option 1 is incorrect because '暗くなる' (to become dark) is an automatic state change, and we say '暗くなり始めた' instead of '暗くし始めました' (which would imply someone actively made it dark). Option 2 is unnatural because 'し始める' is less commonly paired with '〜ところです' (which already means 'about to do') than just 'するところです'. Option 3 is grammatically incorrect: 'テレビを見' should connect to '見始める' (stem of 見る is 見, so 見始める), not '見し始める' which incorporates an extra 'し'.