Impossible to find salvation through the law because of the weakness of the flesh. And you switched from your argument of the law to faith. Of course the law is a schoolmaster to lead us to Christ.
If this were true then none of the OT saints born under the Law could be saved! All the elect OT saints born under Law certainly battled the flesh, but the efficacy of God's grace (including his gifts of faith and repentance) guaranteed their victory. The reason why Israel was for the most part an apostate, rebellious, idolatrous nation is because the [gospel] message they heard from God's prophets (including Moses) was not united with faith (Heb 4:2).
Faith and Law are not mutually exclusive concepts. In fact, for any NC believer the two are perfectly consistent with each other; for the believer knows that he cannot be saved by obeying the law absent any faith! Christians love God's law because they handle the law correctly. They want to obey the Law because they love the Lord and trust him -- and not because they are trying to win God's favor. By God's grace, I have the same attitude towards God holy Law as the Psalmist does in Ps 119, for example.