Ask the broker if they have a record of the purchase. If not, you will have to estimate. If you know approximately when you purchased it, there are web sites with historical stock prices. If all else fails, you will have to use a cost basis of zero, which will make the full amount that you sold it for taxable. However, if your taxable income, after deductions, is low enough, your long-term capital gains might be taxed at 0%, in which case it doesn't matter if you use a basis of zero. After you have entered all your other income and deductions in TurboTax, enter the stock sale with zero basis and see how much difference it makes in your tax.
If you can figure out the date, you can use historical data from NASDAQ or Yahoo Finance to find the selling price on that date.
Does the broker have any info at all for the purchase date?
You can also enter $0 for your cost basis since you do not know what it is. However, this may result in higher taxable income and higher overall tax liability.