dead end

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun An end of a passage, especially a street, that affords no exit.
• noun A street or road affording no exit.
• noun A situation or subject that allows for no progress or development.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun idiomatic A path or strategy that goes nowhere or is blocked on one end.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun a situation in which no progress can be made or no advancement is possible
• noun a passage with access only at one end