Most laptops of that time period used a straight through flex cable with the same pitch connector on both ends, so yours is custom made for that series/model. While there may be other laptops that used the same pitch on the motherboard connector, finding one that would be long enough, and even which model laptop has such a compatible cable, would be a monumental task.
If you could find a flat bed scanner, you could flatten the cable and scan it. Then you could send the scanned image with dimensions and specifications(such as which side of each end has the contacts exposed) to a flex cable house for a prototype quote, and if you could find an inexpensive-enough manufacturer, you might be able to get several samples for less than the price of a night's worth of pints for each sample. You could then re-sell the extras in case anyone else ever wanted the same cable.
An alternative would be to try to repair the cable you have. If only two or three traces are damaged, you might be able to carefully solder enameled wire or wire-wrap wire between the ends of the existing cable, if you can access any copper protruding from the connectors on each end.
A third option, if you wanted to "roll your own", would be to purchase two shorter standard flex cables, which are easily sourced. You would purchase one cable of the proper pitch for each end of your old cable, and then design and etch a thin printed circuit board to adapt the two differently-pitched cables together by soldering the cables to the adapter board.
All of that being said, it may be less trouble to just purchase another scrap laptop of the same model, so that you would also have other spare parts for use later.