The common places for the cable to break are where it enters the keyboard, near the USB plug, or where you ran over it with your chair (happens to us all

)) but it could be anywhere. Plug it in and get it in a position where it's working then carefully bend the cable and listen for the disconnect noise to narrow down where the damage is.
If you have a soldering iron and it's near one end it's a pretty easy job to fix it, just cut the cable and match the coloured wires to where they are in the connector before you desolder the short bit.