Just to make sure (because I'll try anything at this point), I've reversed it and even not used the uplink port. This either didn't help or just shut down the network entirely, as you might assume

Just so -- on a switch (as opposed to router), the only difference between an "uplink" port and a normal port is that the socket is wired reversed, so you don't need a cross-over cable to patch it to a non-uplink port on another switch. When connecting two switches together, you connect a normal port on one to an uplink port on the other; it doesn't matter in terms of functionality which way round you do it, but it'd be less confusing for the next network administrator if the uplink port is the one that leads closer to the actual Internet.
And just out of interest, what on earth (or otherwise) does a church need a 30/5Mbps Internet connection for? That's a lot more than Sigmatel Cambridge ever had...
Peter