Only 1 cord? Is it not a multi-strand cord?
Its sounds as though the blind has been let down in a 'Free Fall' which allows the cords inside to sometimes knot.
If this is the case, you have to look inside the honeycomb approx. 6 -7 inches up and you should be able to see a loose knot in a cord. With a fine wire, make a hook on one end and gently pull the offending cord out at the same time allowing cord to feed in the top. Undo the knot and the blind should work
The BlindGuy, February 2010