The sentence that contains the correct usage of "I" and "me" is:
I believe in the power of you and I.
However, it's important to note that in standard English, the correct phrase should be "I believe in the power of you and me."
The correct form in context should be "you and me" because "me" is the object of the preposition "in." So, the more technically correct sentence would be "I believe in the power of you and me."
If you are simply choosing from the provided options without correction, the answer would be I believe in the power of you and I, but keep in mind that it still doesn't conform to the conventional usage.