The IRC 121 rules would apply to your parents as full owners starting when they obtained full ownership. If they have been living in the property as their principal residence and owning it per IRC 121 they should qualify for the $250k/per person capital gain exclusion. See https://www.law.cornell.edu/uscode/text/26/121
The basis of a property received by a gift is usually the basis of the donor (gift giver). The receiver of the gift is called the donee.
[Exception, if at the time of gift, the fair-market value (FMV) of the property is less than the basis, the donee's basis is the FMV at that time.]
See I.R.C. 1015(a) - https://www.law.cornell.edu/uscode/text/26/1015
The holding period for determining long term vs short term includes the time the donor held the property if the donee's basis is the same as the donor's basis. See I.R.C. 1223(2) - https://www.law.cornell.edu/uscode/text/26/1223
If the value of the gift in 2015 was more than about $14k per donee, then the donor should have filed federal gift tax return on Form 709 (and maybe a state return). If the gift was taxable, the gift tax paid is added to the the basis. But gift tax is rarely paid since it only applies to lifetime gifts over about $11million).
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