The answer is: <span>My neighbor asked my brother and ME to buy bread for her.</span><span>
You can't say: "My neighbor asked I and my brother to buy bread for her", but you can: "My neighbor asked ME and my brother to buy bread for her"!
What is more: if you <em>remove</em> "my brother" there is only one posible answer: "</span>My neighbor asked <span>ME </span>to buy bread for her."<span>
That is why the answer for this sentence is: ME.</span>
My neighbor asked my brother and ME to buy bread for her. Normally it would be I but for this sentence it is me because the English language says that this sentence is grammatically correct.
