Can we free ourselves from the misery of this condition?
No. In our own strength, without divine grace, we cannot do good works pleasing and acceptable to God.
Catechism for the Global Methodist Church, question 47
5Behold, I was brought forth in iniquity, and in sin my mother conceived me.
63The spirit is what makes alive; the flesh helps nothing; the declarations that I have spoken to you are spirit and are life.
14For we know that the law is spiritual, but I am fleshly, sold under sin. 15For what I work, I do not know. For what I will, this I do not practice, but what I hate, this I do. 16Now if I do what I do not want, I agree that the law is good. 17So now it is no longer I who work it, but the sin dwelling in me. 18For I know that nothing good dwells in me, that is, in my flesh. For the desire to do good is present with me, but the ability to carry it out is not. 19For I do not do the good I want, but the evil I do not want is what I keep on doing. 20Now if I do what I do not want, it is no longer I who do it, but sin that dwells within me. 21I find therefore the law, that when I will to do the good, the evil lies present to me. 22For I delight in the law of God in my inner being. 23But I see another law in my members, warring against the law of my mind and taking me captive in the law of sin that is in my members. 24Wretched man that I am! Who will deliver me from this body of death?
17For the flesh desires against the Spirit, and the Spirit against the flesh; for these are opposed to each other, so that you may not do whatever you want.
1And you, who were dead in your trespasses and sins,

Having described the fallen condition, the catechism asks whether people can climb out of it on their own. The answer is the third sentence of Article VII of the Confession of Faith: "In his own strength, without divine grace, man cannot do good works pleasing and acceptable to God." Article VIII of the Articles of Religion, "Of Free Will," is the older form of the same teaching. After the fall a person "cannot turn and prepare himself, by his own natural strength and works, to faith, and calling upon God," and so has "no power to do good works, pleasant and acceptable to God, without the grace of God by Christ preventing us."
The scripture references describe the trap from the inside. Paul's account in Romans 7 is the fullest: "the desire to do good is present with me, but the ability to carry it out is not" (Romans 7:18). He sees "another law in my members, warring against the law of my mind and taking me captive in the law of sin" (Romans 7:23), and he ends with a cry that can only be answered from outside: "Wretched man that I am! Who will deliver me from this body of death?" (Romans 7:24). Galatians names the conflict: "the flesh desires against the Spirit, and the Spirit against the flesh" (Galatians 5:17). Jesus states the conclusion in one line: "The spirit is what makes alive; the flesh helps nothing" (John 6:63). A person who is "dead in your trespasses and sins" (Ephesians 2:1) cannot raise himself.
The word "preventing" in Article VIII is the key to the whole section. It carries the old meaning of "going before." ΒΆ102 of the Book of Doctrines and Discipline calls this God's "prevenient or preventing grace," which "restores a measure of liberty to receive the further graces of God" and is "received prior to our ability to respond." Article VII of the Confession of Faith therefore ends on a second sentence the catechism will pick up later: a person "influenced and empowered by the Holy Spirit is responsible in freedom to exercise his will for good."
For a Methodist, this teaching removes any ground for boasting and any excuse for passivity. Every good work a member does is done with grace that arrived first, so the credit belongs to God; and because that grace has already arrived, the member is answerable for what is done with it. Wesley preached both halves together, and Article VII holds them in one paragraph.