Regardless of 1099-S, you do have to report the sale if any portion of your capital gain is eligible for taxation. Your exclusion amount depends on your filing status.
Put it into TurboTAX and the program will compute your tax, if any. If the tax effect is zero, it is not necessary to remove the reporting from your return.
If the house was your personal residence and you never rented it out, you do not need to report the sale if you did not receive a Form 1099-S. If you ever used the house as rental property or investment property, then you need to report the sale. How you used the house determines if and how you report the sale.
The house was rented for the entire time after I inherited it. However, the house sold for less than the cost basis on my father's date of death. Subsequently, apart from the cost basis and the sale price info, do I need a 1099-S and/or any other information from it to put into TurboTax?
No.
But your cost basis is the Fair Market Value on your father's date of death.