That is not what Calvin taught. There's a crucial difference between total depravity and utter depravity. To say that Calvin and Calvinists teach utter depravity is to bear false witness against them.
Total depravity is where every area of a person - the intellect, the will, the body, the soul, etc etc etc - is touched and tainted and twisted by the effects of the Fall, and by the effects of sin. Let me reemphasize that statement: Total depravity means every area is tainted by depravity. In terms of "doing good things", unregenerate men would do "good" things by accident, as in every case he/she does so with some ungodly desire or end in mind, never with a desire to honor or bring glory to God on His terms.
"Total depravity" doesn't teach that the effects of the Fall apply to just the will. It also affects us physically and psychologically. Reformed evangelist Francis Schaeffer applied this Biblical teaching in a very practical and encouraging way to explain how depravity goes beyond "what we can do" to "what we are". I would encourage you to read them (they are short) here and here.
Total Depravity is probably the most misunderstood tenet of Calvinism. When Calvinists speak of humans as "totally depraved," they are making an extensive, rather than an intensive statement. The effect of the fall upon man is that sin has extended to every part of his personality -- his thinking, his emotions, and his will. Not necessarily that he is intensely sinful, but that sin has extended to his entire being.The unregenerate (unsaved) man is dead in his sins (Romans 5:12). Without the power of the Holy Spirit, the natural man is blind and deaf to the message of the gospel (Mark 4:11f). This is why Total Depravity has also been called "Total Inability." The man without a knowledge of God will never come to this knowledge without God's making him alive through Christ (Ephesians 2:1-5).
-- from the article The Five Points of Calvinism at Reformed.org.