Trying to determine if an old stock certificate has any value

I found an “AMERICAN AIRLINES, INC.” stock certificate dated 1967 in my deceased fathers name in his old safe deposit box. According to a notarized signature on the back of the certificate, it was transferred from my father to me in 1993 when I was a kid.

I got a pointer to the presume transfer agent and wrote a letter of instruction, and followed up with a call. The person I talked to basically kept asking what account number, what address, etc, said they couldn't find anything and told me to write another letter of instruction.

Long story short, before I try to go round and round on this again, can anyone tell me if the 10 shares of common stock indicated on piece of paper could have any value today (other than as a neat collectable)? Or has that likely been zeroed out in the course of the saga of American Airlines business over the years?

Thank you!