The correct answer is A. My father did arrive and I didn't starve.

Explanation:
The sentence is a third conditional statement, which is used to talk about hypothetical situations in the past that did not happen. The structure "If my father had not arrived, I would have starved" suggests that the father did arrive, and as a result, the speaker did not starve. It implies that the arrival of the father prevented the negative outcome of starving.

- A. My father did arrive and I didn't starve: This is correct. The sentence describes a situation where the father's arrival stopped the speaker from starving.
- B. I had to starve because my father didn't come: This is incorrect because the original sentence suggests the father did arrive, not that he didn't.
- C. My father didn't arrive and I didn't starve: This is also incorrect, as the sentence suggests the father's arrival prevented starvation, not that he didn't arrive.
- D. I should have starved but I didn't: This isn't a correct interpretation. The sentence suggests the father arrived, and as a result, starvation was avoided, not that the speaker should have starved.
- E. I had starved before my father arrived: This is incorrect, as the sentence implies that starvation did not happen because the father arrived in time.