You are correct, your cost basis would be the fair market value of the shares when you took possession of them. Often, the broker is not sure what the cost basis is, so they will leave it blank on the 1099-B form.
When you enter the form 1099-B information in TurboTax, you will see an option "I'll enter additional information on my own" on the screen where you enter the cost basis. You should click on that option to enter the cost basis of the investment sales.
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