No the Law isn't sinful.
OP: 2 Cor. 3:6. Explain, the letter kills, but the spirit gives life.
2 Cor 3:7 (A) But if the ministration of death, written and engraven in stones, was glorious, so that the children of Israel could not stedfastly behold the face of Moses for the glory of his countenance; which glory was to be done away:
(NOTE: The ministration of death/law engraved in stones purpose was to expose & without mercy condemn sin. Post sin payment & resurrection is the end of the law for righteousness to all that believe (Rom 10:4)
Gal 3:13 Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is every one that hangeth on a tree:
(NOTE: (NOTE: Faith placed in Christ's sin payment & resurrection REDEEMS believers from the LAW/ministration of death's curses (Deut 28:15-65) & condemnation)
1 John 3:4 Whosoever committeth sin transgresseth also the law: for sin is the transgression of the law.
(NOTE: Sin is the transgression of God's law)
We've all sinned/broken God's law & deserve the sentence invoked in (Rom 6:23 DEATH). No one can say he is not a sinner until some means is provided (not to take away the law) but to remove the sin, which is the transgression of the law.
Matt 7:21 Jesus said; Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; "but he that doeth the will of my Father" which is in heaven.
(NOTE: He that does the will of my Father, shall enter the kingdom of heaven)
What is the will of the Father?
John 6:40 Jesus said; This is the will of him that sent me, that every one which "seeth the Son, and believeth on him" may have everlasting life: and I will raise him up at the last day.
(NOTE: The will of the Father is: BELIEVE in the Son's redemptive sin atoning sacrifice)
Rom 6:14 For sin shall not have dominion over you: for ye are not under the law, but under grace.
(NOTE: Believers that have harkened to the will of the Father, are no longer under the LAWS/ministration of death's curses (Deut 28:15-65) & condemnation)
2 Cor 5:19 To wit, that God was in Christ, reconciling the world unto himself, not imputing their trespasses unto them; and hath committed unto us the word of reconciliation.
(NOTE: Our sins will not be IMPUTED onto us & we're reconciled to God. When we place our faith in Jesus sin atoning sacrifice. Found in His death (sins required wage PAID), burial (proof Jesus died) & resurrection (Fathers receipt, sins payment received & accepted). (See 1 Cor 15:1-4, Rom 10:9-10)
2 Cor 5:21 For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.
(NOTE: Jesus exchanged His sinless righteousness for our sinfulness. And thru faith we become the righteousness of God in Christ)
While the Temple was operating the High Priest had authority to impute/transfer sin (Lev 16:21). Christ is our Great High Priest (Heb 4:14) & has even greater authority to impute sin & righteousness (Rom 4:3-8).