This is what the record online (that now seems to be a match) was:
TAYLOR, Troy William b. 07/11/1911, mmn. Lundy, Male, b. Oklahoma, d. Alameda County, CA, on March 5, 1984, ss#565-07-2810, age 72.
The Cal Birth/Death Indices only give last names of parents, not first names.You can order the death certificate, which should have the full info (as the reporting relative knew it), including where (what state or country) the parents were born.You can find out how to order a birth cert/death cert at www.vitalrec.com.You can use the site to find the proper address for the courthouse that holds the record and the cost, or just order it online through them.
You can do the birth certificate ordering the same way... using the state in which he was born.
As to why you didn't get a match. You may have entered too much information in the search screens.I only entered last name Taylor, first name Troy and narrowed it down from there.
You can also go to www.rootsweb.com and scroll down to social security death index.when you get the search screen, click on ADVANCED SEARCH.... enter only his last and first names and birth date.When you find the record, click on the writing in red on the right to "Order App" or "Write Letter" or something like that.It will generate a letter to the Social Security Administration with your person's info.You then print and mail the letter to the address given with about $7 (the instructions are in the letter you print).By sending this letter, you will obtain his original social security application that was filled out when he was alive, and will probably have full names of birth parents!Be patient, as the ss apps take 30-60 days to be sent.(I've found about 30 days on average before I receive them).