Again, the old isn't made obsolete because obedience of the the law was wrong. The old was made obsolete because it could not efffect the change, the righteous requirement that it, the law, attests to. Man needs something more than himself and his own efforts to do that; he needs God. So the NC isnt about a reprieve from the obligation to be righteous; rather it's the very means to that righteousness. The basic difference between the old and new is, "simply", union with God. That's why Jesus came: to reconcile fallen man with Him. So:
"I will be their God,
and they will be my people.
No longer will they teach their neighbor,
or say to one another, ‘Know the Lord,’
because they will all know me,
from the least of them to the greatest,”
declares the Lord." Jer 31:33-34
"...not having a righteousness of my own that comes from the law, but that which is through faith in Christ—the righteousness that comes from God on the basis of faith." Phil 3:9
Man doesnt need to obey the law first of all-that's impossiple apart from grace, apart from God, anyway. Man needs to turn to God, first of all, in faith, and then from within that union or fellowship He does the fulfilling, the justifying.