Has a country with no navy ever won a naval war against a country that had one?
Short answerNot in a clean example. States such as Rome built naval power, and the American case depended on allied fleets.
NotesThe answer depends on what counts as a country without a navy. Rome built a fleet before defeating Carthage at sea, so it does not satisfy the premise. American independence depended substantially on French and Spanish naval intervention. No clear case of a state with no naval power defeating an opponent in a naval war is identified here.