A difficulty with Calvinism and compatibilism

According to the doctrine of total depravity, we are determined by our sinful desires to reject Christ. We are unable to accept Christ for psychological reasons. Yet we are still responsible for our sinfulness. In fact, according to compatibilism, it's is because our actions are determined by our own desires and motives that we are responsible for them. We are responsible for our actions to the degree that we do them on purpose, and we do them on purpose do the degree that they are determined by our own antecedent psychological states, including our desires, plans, motives, inclinations, preferences, etc.

According to the doctrine of irresistible grace, once God changes our hearts, we are determined by our new desires to embrace Christ. We are unable to resist Christ, again, for psychological reasons. But here's the difficulty. Whereas we could be blamed for our sins and for our failure to come to Christ when we were totally depraved since we acted willfully, on purpose, out of our own sinful desires, etc., we cannot be praised for our decision to follow Christ, even though we do so willfully, on purpose, and because of our desire to do so. The reason is because it is God who changed our hearts.

Irresistible grace is supposed to remove all basis for boasting on our parts because it makes salvation a monergistic act of God. We cannot be praised for our decision to come to Christ because it is God who acted in us to produce that result. Since God brought about the change, he gets all the glory, and there is no room for boasting on our parts.

But surely something causes us to have the desire to reject Christ and to sin. Why should it matter what is doing the causing? Suppose the devil caused us to have sinful desires. Would that mean we're not blamable for sin? Or what if it's just that we inherited a sinful nature or sinful genes or whatever? Somehow or other, something outside of us ultimately caused us to have sinful desires. Yet we are morally responsible for giving into them.

So why is it that if God causes us to have good desires, and those desires cause us to follow Christ, that we are not just as praiseworthy for doing so as we were blameworthy for sinning? In both cases, we acted out of desires that were created in us by external causes.

Jonathan Edwards argued persuasively in his book on the freedom of the will that "The essence of the virtue and vice of dispositions of the heart, and acts of the will, lies not in their cause, but their nature." I wish I could ask Jonathan Edwards about this. I wonder what James White would say. I wonder what John Piper would say. John Piper would probably be a better person to ask since he's a big fan of Edwards like I am.

What do you think?