[President Kimball] told of an experience he had in helping a woman who came to him feeling despondent about the sin she had committed. She said: “I know what I have done. I have read the scriptures, and I know the consequences. I know that I am damned and can never be forgiven, and therefore why should I try now to repent?”
President Kimball responded: “My dear sister, you do not know the scriptures. You do not know the power of God nor his goodness. You can be forgiven for this heinous sin, but it will take much sincere repentance to accomplish it.”
He then quoted to her several scriptures regarding the forgiveness that comes to those who sincerely repent and obey God’s commandments. Continuing to instruct her, he saw hope awaken in her until finally she exclaimed: “Thank you, thank you! I believe you. I shall really repent and wash my filthy garments in the blood of the Lamb and obtain that forgiveness.”
President Kimball recalled that the woman eventually returned to his office “a new person—bright of eye, light of step, full of hope as she declared to me that, since that memorable day when hope had seen a star and had clung to it, she had never reverted to [the sin] nor any approaches to it.”
This reminded me of a talk I recently listened to from Truman G. Madsen, "The Savior, the Sacrament, and Self-Worth". A couple of things stood out to me,
"We often consider ourselves more or less worthless and in some moods, even beyond help, and we approach the sacrament hesitantly and superficially. But worse still. We do not trust the good news. We do not trust the glad tidings. We do not trust the second opinion of the only Physician who will ever finally judge. This is the Christ. This is He who pleads with us to come boldly to the throne of Grace." (emphasis added, See also Heb. 4: 16)
Also this, "Being born again comes by the Spirit of God through ordinances." (Teachings of the Prophet Joseph Smith p. 162). Truman Madsen continues, "It means, as I understand it, that the fullest flow of the Spirit of God comes to us through His appointed channels or ordinances. The sacrament is the central and oft-repeated ordinance that transmits that power to us. Indeed, it is the ordinance that gives focus to all other ordinances."