It would have been nice if the shop had saved a sample of the old fluid that they removed, along with the filter and pics of the material in the pan.
It had been mentioned, in an earlier post, that the trans had been serviced at a Firestone shop, and there is the possibility that they did not use the correct fluid.
I know it may be a long shot, but if the wrong fluid had been put in the trans, and it can be attributed to their service work, if the trans is toast now, it may be worth your while to go back to them for some relief.
Of course, the person that had that original service work done would probably have to make any claim, and since you bought the car, you would have no standing, but the seller might help you out, under the circumstances.
Do you know how long ago Firestone serviced it?