The essence of free will is choosing according to our desires. The will is free to choose whatever it desires. With regard to salvation, the question then becomes, what do fallen human beings desire? Jonathan Edwards said that as fallen human beings we retain our "natural freedom" (the power to act according to our desires), but lose our "moral freedom" (the disposition, inclination, and desire of the soul for righteousness). In the Fall, we lost all desire for God. But because we can still choose according to our desires, we choose to sin and are accountable to the judgment of God. In this sense, the freedom of our will is a curse. All human beings desire to flee from God unless and until the Holy Spirit performs a work of regeneration. That regeneration changes our desires so that we will freely repent and be saved.
This understanding of human free will is not deterministic because determinism teaches that our actions are completely controlled by something external to us, making us do what we don't want to do. This is coercion and is opposed to freedom. How can our choices be determined but not coerced? Beause they are determined by something within -- by what we are and by what we desire. They are determined by ourselves. This is self-determination, which is the very essence of freedom.
(Adapted from Essential Truths of the Christian Faith by R.C. Sproul)