Buzz saw sounds constant through the performance?
This is a little Twilight Zone, but you are listening to a power plug problem in the church sound system.
Broadcast sound systems are designed to run long distances and ignore electrical interference and system mismatches. When somebody is writing large checks for the performance, they don't want to hear from you that the performance is damaged.
You, however, are using home style RCA Red and White cables designed to go 39" (1M) in a carefully controlled home environment.
An environment you don't have.
Solutions are expensive, dangerous, or awkward. You can plug the computer power into the same outlet that powers the church system (awkward). You can turn the power plug over on either the church system or your laptop power (dangerous). You can invest in a couple of high quality audio isolation transformers (expensive). Or invest in a power isolation transformer for either the church or the computer (expensive and dangerous).
There are wacky Solutions, too. You can use any power system on your laptop that doesn't connect to the wall power. A generator would do it as would a power inverter and a car battery.
I know you have no dollars, shekels, pounds, but it's possible some of your church is wired wrong, making it possible for someone to talk to Him a lot sooner than anyone thought by touching the wrong thing at the wrong time.
There is a quicky AC Power Tester available that will tell you if you have wiring problems. It's about the size of a D battery cell and has three lights on it. It's generally about $15 or so. You plug it in and the right sequence of lights has to come on. It's not foolproof, so people have stopped carrying it, but it's a good first step. Somebody in the congregatiopn may have one to borrow.
http://electrical.hardwarestore.com/15- ... 81667.aspx
If you can find this yellow thing by itself...
http://electrical.hardwarestore.com/15- ... 01511.aspx
Koz