In response to the teachings of Arminius, Calvinism developed five points that are known by the acrostic TULIP. The T in TULIP stands for total depravity.
That expression sounds as if it refers to someone like Hitler, Stalin, Mao, or Pol Pot. It sounds as if it refers to someone who is just about as bad as a human being can be.
In its eighth question and answer about total depravity, the Heidelberg Catechism says:
Are we so corrupt that we are totally unable to do any good and inclined to all evil?
Yes, unless we are regenerated by the Spirit of God (see here).
Modern Calvinists do not talk about total depravity in that way. In an article on total depravity, John Piper wrote:
It is true that fallen people can do much good of a moral, social, and cultural nature. They can show love to family, perform acts of kindness, produce great works of art, and make major contributions to civic welfare. However, apart from regeneration by the Spirit, they cannot do these activities to the glory of God. Nor, as a consequence, can they share the exultant joy of the psalmists in the wonders of God’s works (Psalms 19, 145, 147, 148). It requires a radical change, altering the entire bias of the human will, in order to respond positively to the gospel, a change that can be brought about only by the Holy Spirit (see here).
In that same article, Piper indicates that no one is able to respond to God prior to regeneration. This is sometimes referred to as total inability.
A common Calvinist illustration of total inability is a cadaver at the bottom of a deep well. We can throw a rope down and shout for the person to tie the rope around his waist so that we can pull him out. But a cadaver does not hear and cannot respond. The unbeliever is like that. In Calvinist terms, regeneration, the new birth, must precede faith in Christ.
If you believe in Christ for everlasting life, then you are not totally depraved even by the Calvinist understanding. Of course, in Calvinism you cannot be sure that you truly believe in Christ and thus you cannot be sure you are regenerate.
Well, first of all, you can be sure. You are sure if you believe Jesus’ promise of everlasting life (John 3:16; 5:24, 39-40; 6:35, 47; 11:25-26).
Second, the Calvinist doctrine of total depravity is unbiblical. It is not true that unbelievers cannot respond to God. Cornelius, in Acts 10, blows that teaching out of the water. He was not like a cadaver at the bottom of a well before he was born again. As a result of Cornelius’s prayers and alms, God sent him a message via an angel. Cornelius understood God’s message and sent for Simon Peter. When Peter came and evangelized him, Cornelius was born again as a result of faith, not before faith (Acts 10:43-48; 11:14; 15:7-11). In addition, there are over a hundred verses in the Bible showing that faith is the sole condition of everlasting life. I have two chapters in my book Is Calvinism Biblical? (see here) that deal with the issue of total depravity, one of which deals with Cornelius and Acts 10.
If you are not yet a believer in Christ, take heart. You can pray and ask God to show you the way to everlasting life. Jesus is the way (John 14:6), and God will show you that if you seek Him (Matt 7:7-11; Acts 17:27). I suggest you read the Gospel of John and find a solid Bible-teaching church.