My parakeet won't eat her food - what is the most humane way to destroy her?

Did she just stop eating, or did you just get her? If it is the same food she has always had then there might be a problem. If you have changed her food, that is the problem. A bird learns to eat by watching other birds. That way they don't eat something harmful. A bird will probably not try something new unless you slip it into the food it knows in very small amounts. Eventually, the new food becomes normal.