When the "Law" makes us aware we are wretched sinners, that leads us to Christ. To say it only leads those who have been altered by supernatural grace, alters the meaning of the passage. Paul in Romans 7, looking back on his preconversion life knew he was battling to do what he wanted to do, but was not able. Thus, to say our depravity results in an inability to desire God is unbiblical.
Capatibilism is a ruse to sell exhaustive determinism. It says we cannot choose other than what our past dictates, and therefore our corruption precludes us from choosing life when God sets before us life and death and desires us to choose life, Deuteronomy 30:19-20. Thus it rewrites scripture to say God sets death only before some, being unable to choose life, and life only before others, being unable due to irresistible grace to choose death. Thus compatibilism redefines the biblical meaning of choice as non-choice. You cannot make a choice that alters the outcome of your life. Not what scripture clearly teaches.
No, the compatibilist view applies to every illusionary choice we make, according to the ruse.
The answers to your questions concerning the reality presented in the bible as opposed to the reality presented by the philosophy of men can be answered by God's word only if we submit to its authority. If we revise the meaning of words according to man's traditions, we make scripture to no effect.
Does the Bible say we make choices?
Do the choices alter the outcome of our life?
How does scripture read to you? Whoever believes in Him shall not perish but have eternal life. Or whoever God has enabled to believe in Him shall not perish but have eternal life.