blind alley

(noun) a street with only one way in or out. Synonyms: blind alley, cul de sac, dead-end street, impasse.

(noun) (figurative) a course of action that is unproductive and offers no hope of improvement. Synonyms: blind alley. Examples: "All the clues led the police into blind alleys." "So far every road that we've been down has turned out to be a blind alley."