Yes, the false doctrine of Total Spiritual Inability is believed by those who buy into Calvinism and Arminianism.
What is Pelagianism? Also see at the bottom of the above link, a link to What is Semi-Pelagiaism.
Basically Calvinists define these terms so that if you do not accept "Total Spiritual Inability" you believe as historical heretics believed. The ploy is sophistry.
What does scripture teach?
First, as a consequence of Adam's sin, all mankind is made "sinners." Second, just as Adam was "corrupted" when his eyes were opened (to the knowledge of good and evil) all mankind was also "corrupted." Now just what are the results of being "corrupted" and "made sinners" is not specifically described in scripture, and so Calvinists have supplied those results, i.e. Total Spiritual Inability and needing to be "enabled" by Irresistible Grace which compels the individual to seek God and believe in the gospel - the so-called "gift of faith."
If "Total Spiritual Inability" were true, then God would not have needed to harden the hearts of unbelieving Jews,
Romans 11:7. The fact that God did proves conclusively that the "T" of the TULIP is false doctrine.
Then we have Jesus teaching in parables to preclude people from understanding, believing and being saved.
Matthew 13:10-15.
And we have examples of the lost seeking God, such as
Matthew 23:13, but being blocked by false teaching.
Ask yourself if Abraham was enabled by irresistible grace and given his faith in God, why did God need to credit that faith as righteousness? Answer God would not need to credit it for Abraham's sake, nor (
Romans 4:23-24) for our sake.
But what about "no one seeks after God?" Romans 310-12 Here contextually Paul is making the argument that all have fallen short of the glory of God, we all have sinned. When we are sinning, we are not seeking God, so since scripture says no seeks God (all the time or when sinning) this passage supports the idea we all are under sin. Calvinists use the same text to claim no one seeks God (at any time) to support their false doctrine of total spiritual inability.
But what about
Romans 8:6-7:
For the mind set on the flesh is death, but the mind set on the Spirit is life and peace,
because the mind set on the flesh is hostile toward God; for it does not subject itself to the law of God, for it is not even able
to do so,
Here Calvinist make the unsupported claim, unless they have been regenerated, the Fallen are unable to set their minds on any Spiritual things. But again this is reading a self serving limitation into the text. Again I point to
Matthew 23:13 which has unsaved people seeking God (trying to enter the kingdom) thus able to set their minds at least a little of the time on spiritual things.
Well what did the Fall accomplish? The separation from God (because we are made sinners) results with us being spiritually dead, and yes Calvinists redefine that concept to mean unable to seek God and trust in Christ, but again that is an unsupported claim. Thus we need to be born anew, made alive together with Christ which occurs when God places us into Christ. But why cause our corruption, our predisposition to sin? I think the idea is the same as when God reduced the size of Gideon's army in order to increase the glory given to God because of the victory. When a fallen sinner turns to God and trusts in Christ, from a fallen state, that brings more glory to God.
As far as
John 9:39, if we look down to
John 9:41 we see that the Pharisees had enough spiritual ability to be guilty of knowingly sinning. So the very passage cited actually teaches limited spiritual ability.