Hello,
I am also using OBS to livestream my church service and recently gone through the same process of getting audio feed directly form our board.
The issue you are having getting this to work may have to do with the 3.5mm port you are using on your computer. Most desktop computers have 2 separate 3.5mm ports; one for a headphone connection (usually a light green color) and another for a microphone input (usually a light pink color).
If you are using a desktop computer, be sure to connect the 3.5mm cable to the pink connector in order to input sound to your PC.
If you are using a laptop or your computer only has only one 3.5mm port, then you will need a splitter that's connects to that 3.5mm port and allows you to connect a headphone and mic separately (these adapters usually come with computer headsets that's have mics). With that, you need to connect the 3.5mm cord form the sound board to the mic input in the splitter (again usually color coded as light pink on the splitter). If you don't have one, you can find them online by searching 3.5mm headseat splitter.
In my case, being on a laptop, I needed to use that splitter and I was able to get it to work (although I am currently diagnosing a problem with horrible interference/static coming from the feed).
I hope this helps. I understand this may be common knowledge for some so forgive me if this is not relevant to you.