What do I enter as the vehicle total cost if the vehicle was given to us for our business? We paid nothing for it. Should I used the fair market value?

Your basis in a car for figuring depreciation is generally its cost. In your case, the cost is zero (0).  TurboTax asks the cost in order to calculate depreciation (if you choose to use actual expenses instead of mileage).

However, according to IRS Pub. 551 - Basis of Assets: 

If you hold the gift as business property, your basis for figuring any depreciation, depletion, or amortization deduction is the same as the donor's adjusted basis plus or minus any required adjustments to basis while you hold the property.

If the donor used the car for business, they should be able to tell you the adjusted basis.  If they did not use it for business, use the fair market value at the time of the gift.

For additional information, see IRS Pub. 551 - Basis of Assets.