Agree with Bhai that this is not the GMAT type. The answer is E (or A - both are same....there are only 4 choices for this question.). Anyways, I think the question is to especially elaborate the foll concepts.
1. Look at the second part of the sentence. Technically you can rewrite it as 'I was the thief'. You cant rewrite it as 'me was the thief'. So, 'I' is right for the second part.
2. the first part of the sentence is tricky...'but' is a preposition here and not a conjunction. Why? becuase, you can rewrite the first part as 'No one could have told them that, but him'. This makes 'him' right too.
Thanks for trying