1. "He who sings once, prays twice." St. Augustine's famous quote really does come in handy. Most people have heard this before and can easily grasp the concept. Putting a prayer to music can enhance and amplify the emotions associated with the text, and it is this emotional connection to God we are seeking with our communal prayer.
2. Singing in a large group develops a sense of oneness with others in the group. When we all breath at the same time and sing the words in unison, we are crying out to God as a community, not just as individuals. We can attempt this with spoken prayer, but I usually hear some people rushing ahead, or lagging behind. The beat of the music solves that problem and brings us all together.
3. I often call to people's minds an image of a birthday party where no one sings "Happy Birthday." What a dismal celebration that would be! No, even those who have difficulty carrying a tune sing Happy Birthday with gusto at a party because they want to add to and be a part of the creation of feelings of good will for the person celebrating a birthday. Our Church service is also a celebration!
When you speak to your congregation, do so without reading from a script. Speak from the heart. These three points are easy to remember and motivating to hear. If you currently have a non-singing congregation, I think just an occasional reminder of why we sing will make a difference.