I didn't want to work (without pay) for that non-profit for the rest of my life, and if I had, I would've had to deal with their small-time local IT service provider, and it was already a nightmare prior to a hypothetical initiative like me standing up computers or servers of my own.
My experience with small (non startup) organizations, meaning under a dozen people, is limited, but it's led me to believe that every role in that situation is like being a high level executive, only without the pay of a big corporation or an assistant (other than the volunteers...).
They might have had a place for me if I had been able to wrangle their hostile service provider, but doing technical things wasn't what they needed. I couldn't even start if all their servers and their network were under the control of someone who wouldn't talk to me.
They would've been happy if I could've dealt with their domains, and everything else related to IT, but at a administrative/managerial level - it was entirely about talking to people, and I was keenly aware I didn't know where to start.