I don't believe this is the kind of question that can be answered with a "13th of Whenever, A.D. XXX". Nor even by pointing to a specific council, or the ruling of some pope. This is because the problems that make Rome a false religion are many and varied.
An analogy would be to a dying person--several things are killing him: 1) age, 2) lifestyle, 3) cancer, 4) heart disease, 5) scurvy, 6) polio, and 7) pneumonia. And add a few other problems into the mix. You go visit the guy one day, and he's managing. Another day, and he's deteriorating. You pass the cemetary one day, and you notice there's a headstone there with his name on it. What killed him? What pushed him over the edge? One thing, and everything. He kept picking up opportunistic infections. It was, uh, the 12th problem he had that actually stopped his ticker. But he had a total of 24 issues. And #12 is usually not fatal in 99% of people who get it.
I'd say when you dethrone Scripture as the sole, final authority in making theological decisions, you have stopped listening to God alone. You've stopped listening to the Great Physician. You weigh his counsel along with all the other experts. Eventually you make it against the law for sick people to inquire straight from the Doctor. They can only come to you to get a pre-written prescription from the approved list of remedies. A fairly short list, too. If your symptoms aren't on the list, you aren't sick. Everything fits into a few broad categories. Plus, if you come each day, week, or year and take a dose of tonic you shouldn't get sick!
Look at Rome's problems: sacerdotalism, sacramentalism, papal imperium (eventually, Luther diagnosed this as the root illness in his opinon), idolatry, Marianism, syncretism, traditionalism, corruption of the true sacraments in form and substance, proscribing the Scriptures, rote worship, worship in an unknown tongue, ...
Look, even if some of these things have been recinded today, that's like saying some disease or other ran its course, and is no longer present in the patient.
I would say this: in Augustin's day, the western church had its problems already, particularly in the realm of hierarchy and sacramental corruption. But even that corruption was not nearly as far gone as it would eventually get. And Augustin had the Scriptures which he weilded against heresies with alacrity.
One of the problems we face as historians is that the official records usually can't tell us what individual piety was like. Or what differences were held between the highest leadership, and a local church and its leadership. To say that everyone believed and followed the innovations of Rome immediately, is to suggest that when historians examine our age (many years from now) they might assume that Willow Creek ideology or TBN was the "20th century America" church-theology and practice. Everyone was into "name-it-and-claim it" and "church growth" methodologies, and preacher scandals were the norm. What I mean is, we have to acknowledge there was a trend in the ancient and medieval church, a trend that we know wasn't followed by everyone given some of the "heretics" Rome identified over the centuries. The Waldensians/Piedmontese are a remarkable example of pockets of the church that retained more of the gospel than the main branch.
But sometime in the middle ages, sometime between 517 and 1517--between the adoption of semi-Pelagianism (contra Augustin), between monasticism, between Latin rites, between abandonment of preaching the Bible, between the thorough politicization and debauchery of the pontificate, between the Great Schism, between paying $ for indulgences, between pilgrimages and fasts and church calendars, between the multiplication of sacraments (7 is a scaled down number),...
Between all that junk, Rome was completely off the rails. And Luther's mild, academic call for reform was met with bared tooth and claw. Too bad for Rome, this was the Lord's doing; and marvelous in our eyes was his repairing the whole breach. In a remarkably short period of time--say, about 50 years--in some places it was actually possible to find churches that resembled a truly apostolic church, a reformed church according to the Word of God.
Post -Reformation, the papists tried their own hand at reform, the Counter-Reformation, but they had set groud rules going in. Certain things were untouchable. And in the end, all they could do was treat symptoms and not the disease. Because going in they had decided that contra the Reformers, Rome was not fundamentally broken, wheels off the chariot, etc. Like their semi-Pelagian theology of the individual, ecclesiastically Rome was "basically sound."
So, I think that the Council of Trent essentially made the false religion that was already the basic orientation of Rome, her official and permanent stance. She was operationally already a cult, and now Rome was irreformable. The faithful church is already outside Rome's ruins. Both the oldest church-bureaucracies, the East and Rome, are saddled with enough dead wood that I do not see them ever successfully reforming. But that's OK, because God has sent the Protestants into their lands to evangelize. Eventually, those false churches will disappear. They may be replaced by other false churches, given our sinful proclivities, but their coercive power is only dangerous when they are allied with the state, or field their own flesh-and-blood armies. Spiritually, Rome is as moribund as a vast cemetary.