I think you must have misread whatever you were reading. The verses you are citing would not be an especially suitable prooftext for total depravity. I think what you are reading was more likely referring to Romans 7:18-21.
For I know that in me (that is, in my flesh,) dwelleth no good thing: for to will is present with me; but how to perform that which is good I find not. For the good that I would I do not: but the evil which I would not, that I do. Now if I do that I would not, it is no more I that do it, but sin that dwelleth in me. I find then a law, that, when I would do good, evil is present with me.
Maybe that is not what they had in mind either, but you see how that is a much better prooftext.
Now, you said regarding total depravity, “I’ve been researching presuppositional apologetics a bit, and it seems to be based on the Calvinist teaching that original sin is total depravity; we can not make a decision to accept the grace of God in the state of original sin; God must change us so that we can accept His grace.” While Catholic theologians have often denied the excesses of Protestant teaching on original sin, the doctrine of original sin was not a dividing issue between Catholics on one hand and the Lutherans and Calvinists on the other. The only condemnation of Lutheran-Reformed teaching in the Council of Trent’s Decree on Original Sin was this:
If any one denies, that, by the grace of our Lord Jesus Christ, which is conferred in baptism, the guilt of original sin is remitted; or even asserts that the whole of that which has the true and proper nature of sin is not taken away; but says that it is only rased, or not imputed; let him be anathema. For, in those who are born again, there is nothing that God hates; because, There is no condemnation to those who are truly buried together with Christ by baptism into death; who walk not according to the flesh, but, putting off the old man, and putting on the new who is created according to God, are made innocent, immaculate, pure, harmless, and beloved of God, heirs indeed of God, but joint heirs with Christ; so that there is nothing whatever to retard their entrance into heaven. But this holy synod confesses and is sensible, that in the baptized there remains concupiscence, or an incentive (to sin); which, whereas it is left for our exercise, cannot injure those who consent not, but resist manfully by the grace of Jesus Christ; yea, he who shall have striven lawfully shall be crowned. This concupiscence, which the apostle sometimes calls sin, the holy Synod declares that the Catholic Church has never understood it to be called sin, as being truly and properly sin in those born again, but because it is of sin, and inclines to sin.
You can see that the fundamental disagreement is really rooted in the errant Protestant doctrine of justification rather than the Protestant doctrine of original sin. Other than that, this is only really a rejection of imprecise Protestant terminology.
Catholics might not agree with “total depravity” depending on how it is defined, but according to your definition of it, it would have to be confessed as a basic principle of Catholic orthodoxy. The Council of Trent in its Decree on Justification, while acknowledging that justification and regeneration are not without the consent and cooperation of man, declares the need for the unmerited prevenient grace of God as the beginning of man’s justification.
The Synod furthermore declares, that in adults, the beginning of the said Justification is to be derived from the prevenient grace of God, through Jesus Christ, that is to say, from His vocation, whereby, without any merits existing on their parts, they are called; that so they, who by sins were alienated from God, may be disposed through His quickening and assisting grace, to convert themselves to their own justification, by freely assenting to and co-operating with that said grace: in such sort that, while God touches the heart of man by the illumination of the Holy Ghost, neither is man himself utterly without doing anything while he receives that inspiration, forasmuch as he is also able to reject it; yet is he not able, by his own free will, without the grace of God, to move himself unto justice in His sight. Whence, when it is said in the sacred writings: Turn ye to me, and I will turn to you, we are admonished of our liberty; and when we answer; Convert us, O Lord, to thee, and we shall be converted, we confess that we are prevented by the grace of God.
There are also many places in Scripture which make this clear. Here are a few.
*]No man can come to me, except the Father which hath sent me draw him (John 6:44)
*]Ye have not chosen me, but I have chosen you (John 15:16)
*]Being confident of this very thing, that he which hath begun a good work in you will perform it until the day of Jesus Christ. (Philippians 1:6)
*]For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: (Ephesians 2:8)