For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
Sometimes Paul’s words are “hard to understand.” (2 Pet 3:15, 16) In some cases, it appears that Paul disparages the Torah, relegating it to something that has exhausted its usefulness and has been replaced by something better. The difficulty is heightened all the more when his teaching in other places seems clearly to extol the Torah as the standard of righteous living for all of God’s people.
In 1 Tim 1:8-11, Paul appears to be saying that God gave the Torah for the sole purpose of condemning the unrighteous and that it has no positive application to those who are righteous.
Yet Paul’s statement elsewhere that the Torah is “spiritual” (Rom 7:14) suggests that it has a positive application to those who have been born again by the Spirit. For Paul, only believers in whom the Spirit dwells are able to appreciate spiritual realities (1 Cor 2:9, 10).
If we loose the doctrine of salvation by grace though faith alone we have lost the battle. Salvation then comes through some form of good works instead of Jesus finished work on the cross alone. It is another gospel. (Gal 1:6-10). Paul wrote the whole book of Galatians on it, and much of Romans. False teachers are all over the internet and elsewhere.
Those different statements are easily reconciled. The law was good and holy given by God (Rom 7:12), yet following it could not make people perfect (Heb 7:19). Following the law could not save us, yet it could and did show our sin and need of a savior (Rom 7:7-13). It could and did point to Christ. It was like a guardian when we were young, but we are no longer under its tutelage now that we have faith (Gal 3:24-25).
Paul calling the law spiritual in Rom 7:14 refers to its divine nature. It is not flesh and blood. It was given and inspired of God, not a list of rules made by man. He was not saying that obedience to the law was equivalent to 'walking by the spirit', which is actually contrasted with the law (Rom 8:3-5, Gal 5, Rom 7:5-6, Gal 4:21-31, etc).
Paul does not say anywhere that it would be wrong to obey the law, nor did he ever say that the Old Testament was useless in our walk with God. All scripture is God breathed and profitable. He never encouraged Jewish converts to abandon their Jewish heritage, either.
However, the law could neither save nor perfect man. We are not justified through keeping the law, but through faith in Christ (Gal 2:16). We grow by adding knowledge to faith, virtue to knowledge, etc (II Pet 1:3-11).