A signal path usually goes like this: Source - Mic/DI - preamp - eq/effects - interface/soundcard - software/recording device
You've got the source, the Mic/Di, Pre's and Eq down, now that you need to do is take the mix down from your sound board and get it go into your existing soundcard (NOT the best method) or use an interface or upgraded soundcard and record it using the Laptop.
If you need to use what you got cause of the lack of funds, I would say (and I've done this at church) that you should use an Auxilary channel or bus and run it into the LINE in on your laptop. Take some time before the service and make shure you're careful about setting the level so you don't clip (distort). It'll be easy with a stock soundcard.
The better option is to get an actual interface, either Firewire, PCI or USB and use that to take a signal from the board into the software. Presonus and M Audio make great products for this. All you need is two channels and you'll be able to record your service in stereo!
Jacob