Does it mean that it is unknown to Fidelity or that it just did not make it to the 1099-B?

Unknown to Fidelity.  Not uncommon if you changed brokerage firms and the security was purchased before I think 2011.

Was purchased before 2011 as the stocks put in our account were a gift from family. We have no idea when the original purchase date is.

Need to ask the person who gifted you the stock as to original date and cost basis of this gift.  The givers cost basis remains with the stock gift.  Cost basis is more important than date.  You can provide a good faith estimate of date.
Or was the stock an inheritance?

No not an inheritance was a gift.

TurboTax won't let me put in unknown?  What amount do I put in the cost basis box?

 

If the basis is unknown that means that the broker does not know what you paid for the security.  If you have no idea either - and no way to find out - then you will have to put zero in the basis.  That means you will pay taxes on the full amount that you sold it for.