If its a clean break (e.g. you havent snapped any of coloured circuit board off) then you should just be able to solder the 4 connections to join the silver bit to the usb stick.
You may have problems soldering the original silver end on, so buy a cheap extension lead and chop off the female end and solder the wire directly to the usb sticks circuit board.
Good luck
Antony, December 2008