You may be able to get a replacement lead from the manufacturer, but if not, you could always ask either someone you know that is competent with a soldering iron, or maybe an electrical shop if they can remove the broken part of the lead and replace it? You may loose the function of the buttons on the cord, but its better than throwing them away! I have repaired many sets of headphones in the past, just because i cant bear to throw them away when its only the cord that is broken.
Good luck, best regards,
K.