The purchase price for the donation of inherited stock would be the stock basis when you inherited it, not the original purchase price. You would be limited to deducting your basis in the stock because you held it for less than a year.
The basis of inherited property is generally the fair market value (FMV) of the property at the date of the individual's death, unless the estate uses an alternate valuation. This is called the "step-up-basis."
The stock would have a step-up basis from 1988 when your father passed, but that would be adjusted to the FMV as of the date your mother passed. Most stockbrokers can provide you with historical stock prices for this purpose.
For more info, see IRS Pub 551 Inherited Property Basis