The English Puritan Thomas Boston (1676-1732) provides a helpful insight into the relationship between human inability and responsibility in his Human Nature in Its Fourfold State (reprinted by Banner of Truth Trust, 1964).
Objection 3: But all this [repentance/faith/etc] is needless seeing we are utterly unable to help ourselves out of the state of sin and wrath. Answer: Give not place to that delusion, which puts asunder what God has joined, namely, the use of means and a sense of our own impotency. If ever the Spirit of God graciously influence your souls, you will become thoroughly sensible of your absolute inability, and yet enter upon a vigorous use of means. You will do for yourselves, as if you were to do all, and yet overlook all you do, as if you had done nothing. Will you do nothing for yourselves because you cannot do all? Lay down no such impious conclusion against your own souls. Do what you can; and, it may be, while you are doing what you can for yourselves, God will do for you what you cannot (196-197).
God has promised that anyone who believes in Christ will be saved. Our unregenerate state is so desperate that we need God’s blessing to even turn to Him in faith. However, this fact should never encourage inaction. When the gospel is presented, the lost must simply repent and believe. God will help their unbelief.