What defines Protestantism? What are the core tenets that would define a Church as being Protestant?
There are five "solas" (only's) that are the tenets of Protestantism.
Sola Scriptura (Bible alone, as opposed to Bible and Church)
Sola Fide (Faith alone, as opposed to faith plus works)
Sola Gratia (Grace alone)
Sola Christus (Christ alone)
Sola Deo Gloria (To God alone be the glory)
To the best of my understanding, the Catholic church agree on the last three, so that it is only the first two that have been points of contention.
In recent years, there have been dialogue between the Catholic church and the Lutheran churches over faith alone, and the consensus is that the divide has been largely one of misunderstanding over the word justification. When Lutherans say justification, they are speaking of initial justification, that moment when a person first becomes a Chrisitan, whereas Catholics are almost always speaking of ongoing justification, that grace that helps them continue to live their lives as Christians. Both sides agreed that Initial Justification was faith alone, and that Ongoing Justification involved works as well as faith.
So the only sola that is left is Sola Scriptura, or Bible Alone. It is an issue of who or what is the authority for doctrine.
The Catholic church points out that in the early church there was no New Testament. Christians depended on the authority of the bishops to determine doctrine. The bishops got their authority via the laying on of hands in an unbroken chain going back to the apostles. This laying on of hands indicated that they were appropriately taught and could be trusted to teach rightly. This unbroken chain continues to today. Part of accepting this authority is accepting the New Testament, which the bishops canonized -- Chrisitans would not have the New Testament if it were not for the authority of the bishops.
Protestants utterly reject this authority. For them, decisions in doctrine can be based only in the scripture. When a question arises such as whether or not an infant should be baptised, they will not go to early church fathers, but only to the authorized New Testament canon. Now of course its not like Catholics will not also go to the New Testament -- they simply interpret it differently. But a Catholic will consider both the New Testament and the church fathers contributing to what they call the deposit of faith. Protestants are like, YUCK!
Evangelicals are even more extreme about the Bible, seeing it as the answer to all, or perhaps most of life's questions. You can perhaps sum up Evangelicalism as:
B-I-B-L-E Yes that's the book for me. I stand alone on the word of God. the B-I-B-L-E
So there you have it. The big difference between Catholics and Protestants boils down to what is the authority. All the other difference such as Marian doctrines, Purgatory, etc., can be chocked up to that.