Taxpayer dies in February, 1982. At the time she has AT&T stock. I have the stock price for AT&T in Feb 1982, but I dod not know the number of shares owned at death. The State Comptrollers Office finds the beneficiary in 2013 and pays her approx $75,000 in unclaimed funds money. At the end of 2013, the Estate gets 14 1099B's from the State which show the sale date, amount, and number of shares from 14 different Telecom companies (probably AT&T spinoffs). We have no records from the deceased. What logical method can I use for calculating the Cost Basis for the 1099B's the Estate received? Any suggestions?

needless to say, say you bought the shares yourself, your basis is what you paid for the shares, including brokerage commissions and of course different rules apply if you inherited the stock or received it as a gift. as you don't have that paperwork, then you'll have to take a few more steps to track down the cost. It's worthwhile to find out how much you paid -- otherwise, you'll get stuck paying taxes on the total value when you sell the shares rather than just on the earnings, leaving you with a much bigger tax bill than you actually owe. You may contact those brokers since they must keep records for six years, and some go back further.
If the brokers don't keep records that far back, you can try to remember when she bought the shares and see what they were selling for then. A stock certificate might be dated or old tax returns might show when she began reporting dividend income. Then you may look up historical price quotes. Or I guess you can contact; PG&E’s site has a ton of good resources, including stock split and dividend history going back to 1912 and historical price going back to 1980. The site also has the contact information for the shareholder services department, which might be able to answer your questions about the share price before 1980.
PG&E Corporation - Stock Info - Quote & Chart