In the year 2005, this is still one of the most controversial passages in the New Testament. Believe me, nothing I can say about it will settle the dispute in your church. But I may be able to settle your mind a bit.
We know from other passages in Paul’s letters and the New Testament that these verses cannot mean that women are never to utter a sound in church. For instance, note that Priscilla was praised as one of the teachers of Apollos (Acts. 18:26; Rom. 16:1–5; 1 Cor. 16:19). Additionally, in the same letter to the church in Corinth Paul notes that women are praying and prophesying and does not condemn the practice (1 Cor. 11:5, 11).
Clearly in this letter Paul has to address several notions that were incorrect; for example, some of the saints boasted, “Everything is permissible for me!” (1 Cor. 6:12; 10:23). That was a slogan based on a half-truth. Paul countered with several basic principles of Christian living, such as, “not everything is beneficial,” and “I will not be mastered by anything.” One possible interpretation of the passage you mention is that the idea that women should be mute is one of these incorrect notions.
Another reason why I think this was a false teaching that Paul sought to correct is that those who propounded it appealed to “the Law,” but nowhere in the Old Testament are women told to keep quiet. 1 Corinthians 14:36 has to be considered in context here; this is Paul’s rebuke to those who would silence women: “Did the word of God originate with you? Or are you the only people it has reached?”