Hence we must conclude that the law has a two-fold office, in accordance with the fact that there are two classes of men?

Yes, in regard to unbelievers it seems but to convict and make them inexcusable before God (Rom 3:3). And this is what Paul says, that it is the ministry of death, and condemnation (2Co 3:6,9). In regard to believers, it has a very different use.