"And although you were dead in your transgressions and sins, in which you formerly lived according to this world's present path, according to the ruler of the kingdom of the air, the ruler of the spirit that is now energizing the sons of disobedience, among whom all of us also formerly lived out our lives in the cravings of our flesh, indulging the desires of the flesh and the mind, and were by nature children of wrath even as the rest… But God, being rich in mercy, because of his great love with which he loved us, even though we were dead in transgressions, made us alive together with Christ – by grace you are saved! – and he raised us up with him and seated us with him in the heavenly realms in Christ Jesus, to demonstrate in the coming ages the surpassing wealth of his grace in kindness toward us in Christ Jesus. For by grace you are saved through faith, and this is not from yourselves, it is the gift of God; it is not from works, so that no one can boast. For we are his workmanship, having been created in Christ Jesus for good works that God prepared beforehand so we may do them." – Ephesians 2:1-10
"Do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived! The sexually immoral, idolaters, adulterers, passive homosexual partners, practicing homosexuals, thieves, the greedy, drunkards, the verbally abusive, and swindlers will not inherit the kingdom of God. Some of you once lived this way. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God." – 1 Corinthians 6:9-11
All of us were dead in sin. You're by no means alone in having a past shameful to God. And that's okay today. God knows that. Indeed, He is great through that, because by all your failures then, His mercy shines as all the more great. None of us can even begin to deserve God's forgiveness. But that's okay, because it is God's initiative. Like Paul said, "You were dead...But God!" That's the brilliance. God had mercy. God loved. Your sins didn't keep God from saving you, and they can't keep you apart now.
"Therefore we have been buried with him through baptism into death, in order that just as Christ was raised from the dead through the glory of the Father, so we too may live a new life. For if we have become united with him in the likeness of his death, we will certainly also be united in the likeness of his resurrection. We know that our old man was crucified with him so that the body of sin would no longer dominate us, so that we would no longer be enslaved to sin. (For someone who has died has been freed from sin.) Now if we died with Christ, we believe that we will also live with him. We know that since Christ has been raised from the dead, he is never going to die again; death no longer has mastery over him. For the death he died, he died to sin once for all, but the life he lives, he lives to God." – Romans 6:4-10
"I will sprinkle you with pure water and you will be clean from all your impurities. I will purify you from all your idols. I will give you a new heart, and I will put a new spirit within you. I will remove the heart of stone from your body and give you a heart of flesh. I will put my Spirit within you; I will take the initiative and you will obey my statutes and carefully observe my regulations." – Ezekiel 36:25-27
You are a new creation. You don't have to worry about "turning over a new leaf," because God killed your old leaf on the Cross with Christ and is making you a brand new one! Of course you can't change and become more holy; no one can! This happens by the power of God, and He promises if you trust Him that He will conform you to the image of His Son. He will make you like Jesus if you are His, no matter how long it takes or how painful or sloppy the process. He will do it. And all of God's promises are a "yes" through Jesus Christ.
"He was wounded because of our rebellious deeds, crushed because of our sins; he endured punishment that made us well; because of his wounds we have been healed. All of us had wandered off like sheep; each of us had strayed off on his own path, but the LORD caused the sin of all of us to attack him. He was treated harshly and afflicted, but he did not even open his mouth. Like a lamb led to the slaughtering block, like a sheep silent before her shearers, he did not even open his mouth. He was led away after an unjust trial – but who even cared? Indeed, he was cut off from the land of the living; because of the rebellion of his own people he was wounded. They intended to bury him with criminals, but he ended up in a rich man's tomb, because he had committed no violent deeds, nor had he spoken deceitfully." – Isaiah 53:5-9
You may say you don't understand how God could forgive you and forget the past. The Cross is how. When Jesus was on the Cross, a transaction was made. All of your sins—every single one in the entire course of your life from birth to death—were placed on His shoulders. God's not overlooking your sin; instead He took its horror into Himself through His Son and annihilated it with His wrath. All of your sins have been completely and justly punished. But the punishment was borne by Jesus and not you, because that is the love of Christ, one who gave up His life for His friends. So God's not just flippantly ignoring or writing off your sins. He took them from you, poured wrath on them, and destroyed them. You are free. Jesus Christ has destroyed your past; it is no more. So be free! Be happy! Your sins are truly and completely forgiven!