The latest training videos produced for the webcast equipment describe the various places typically used in buildings to get an audio signal. Basically, check in order, the pulpit, the sacrament table (underneath), or a satellite rack (if you have one). The satellite rack is typically RCA output and tends to have a hum, that can be eliminated with a ground-loop eliminator available at most Radio Shacks. Under the Sacrament table (or old clerk table if you have one) is where audio recordings used to be made with a tape recorder. In my experience, as recording meetings/blessings, etc.. fell out of practice in our church services, these connections were easy for FM to just CUT and figure nobody uses them so when we re-did the sound system 5 years ago, we didn't...blah, blah, blah... (5 of my church buildings are in this situation, no audio comes out the audio out). If you have a newer building you may get this at the pulpit.
In the new proto-type building here in Kansas City, the Tech closet has an Ethernet cable, and video/audio(stereo) out right there. The only cable I need now is (1) for RCA Video, and (1) RCA to Mini converter for Audio. (At least for a functional broadcast without all the bells and whistles.
“A long habit of not thinking a thing wrong, gives it a superficial appearance of being right, and raises at first a formidable outcry in defense of custom.”
― Thomas Paine, Common Sense