The player sprite class contains a dead_end function that checks to see if the player can move up, down, left, and right.  If the player can only move in one direction, the dead_end function returns True.

To check whether the player has reached a dead end, add the following lines to your main while loop after the player/finish line collision checking and before screen.blit(background, (0,0)):

    # Check for player in dead end
    if player.dead_end(block_sprites):
        game_over = True

The above code ends the game by default if the user goes into a dead end.  Change the line 'game_over = True' to be whatever you want to happen.