Problem: If "The path to the lake was blocked, so we couldn't use it.", is "We couldn't use the path." correct?

Answer: yes


Problem: If "Sam pulled up a chair to the piano, but it was broken, so he had to sing instead.", is "The piano was broken, so he had to sing instead." correct?

Answer: yes


Problem: If "Sam pulled up a chair to the piano, but it was broken, so he had to sing instead.", is "The piano was broken, so he had to sing instead." correct?

Answer:
yes