What is the ruling regarding a father's vow to sacrifice a sheep upon purchasing a car, which he did not fulfill at the time, and now finds it difficult to fulfill, and does not remember the exact wording of his vow?

Slaughtering is not obligatory due to a vow unless the one who made the vow restricted it to being an act of closeness (to Allah), such as being a charity or for distributing its meat to the poor, whether by utterance or intention. If your father's vow was restricted by something that implies closeness, then he must fulfill it, and his obligation is not absolved except by slaughtering what he vowed. The fact that he did not pray during that period does not prevent his vow from being valid. However, if it was merely an intention without utterance, or an utterance that does not indicate a commitment to an act of closeness, then nothing is binding on him. And if there is doubt about the occurrence of the vow or the validity of its wording, then nothing is binding on him, because the default is the absolution of responsibility.