The usual rule, for a gift, is that the recipient's basis is the giver's basis (what you parents paid for it). But there is an exception for the gift of your parent's home, where they retained the right to live there ("life estate"). "If they give away part of the home and keep a life estate in that home..... the cost basis of the house is "stepped-up" to the value of the house on date of death [IRC 2036]")
More info: http://www.law.cornell.edu/cfr/text/26/20.2036-1
A life estate does not have to be explicitly established in the deed. Your parents probably had an "implied life estate." If so, that would give you the stepped up basis. There is case law on this.
http://accessiblelaw.org/Documents/LifeEstates-Inheritances.pdf
You may want to Check with a lawyer.
