I am trying to retrieve an old Yahoo mail password, is this possible?

If you have another email address, see if you can have them send it to you at that address.

Every time I do that the system ask if I added this email addy at the time of opening that particular account. Which I did not. What do I do.

Easiest way to to simply follow the Forgotten Password links that's available on the Yahoo sign in page.
If you can answer the security questions correctly then the account will be open to you.
If not then you'll have to plead your case to Yahoo directly.
Your cahnces of the latter working are next to NIL.