From my understanding of scripture, our depravity is deep and at the heart of our desperate need for a Saviour. Paul writes the following to the Ephesian church:
'And you He made alive, who were dead in trespasses and sins, in which you once walked according to the course of this world, according to the prince of the power of the air, the spirit who now works in the sons of disobedience, among whom also we all once conducted ourselves in the lusts of our flesh, fulfilling the desires of the flesh and of the mind, and were by nature children of wrath, just as the others.' Ephesians 2:1-3
We were dead, sons of disobedience and children of the wrath of God. These are strong words, reminding us of the sinfulness that we are steeped in. That our nature carried death, the very opposite of who God is. Sin leads to death, and Paul said we were all dead. We were utterly lost. In Rom 6:20 Paul again refers to us as being slaves to sin, overpowered by this master called sin, unholiness and fallen nature.
Isaiah 64:6 states that,
'But we are all like an unclean thing, And all our righteousnesses are like filthy rags; We all fade as a leaf, And our iniquities, like the wind, Have taken us away.'
Our best attempts to be righteous without the redemptive work of the cross in us is impossible, ‘for all have sinned and fallen short of the glory of God’ (Rom. 3:23). There is no good in us apart from God’s grace (Ps. 16:2). The way I understand it is that just as we can sin as a born again believer, we were able to do good deeds as unbelievers. Good deeds, however, do not change our nature or state of holiness. That can only be found and done through accepting the redemptive work of Jesus in our lives.