You are right. The Law is not broken up into parts. The Law includes EVERYTHING. All 613 Commandments. Obviously we are not under the Law anymore because Jesus made many changes. He said turn the other cheek instead of an eye for an eye. God told Peter to eat unclean animals when it was against the OT Law. So yeah, the OT Law is not binding as an entire package anymore like it used to be.
But this does not do away with the Law of love in the New Testament (Which is taken from the Old), though. For I think you missed what I said before. Romans 13:8-9 says, Owe no man any thing, but to love one another: for he that loveth hath fulfilled the law. For this, Thou shalt not commit adultery, Thou shalt not kill, Thou shalt not steal, Thou shalt no bear false witness, Thou shalt not covet; and if there be any other commandment, it is briefly comprehended in this saying, namely, Thou shalt love thy neighbour as thyself.