We spent some time troubleshooting today and we had to conclude that the problem is not with any of our gear or wiring. Either the new modem is also not working or the wiring is messed up outside of Omni (possibly the fault of the construction across the street) or the equipment at AT&T / LMI (our ISP) is messed up.
This will likely take days to fix so we are trying to arrange for a backup internet connection tomorrow. We will likely have some form of internet tomorrow evening.
Technical details:
The new modem lit up one of its two DSL connection lights, meaning that one of the two phone lines connected. It then lit up its Internet light which I believe means that it has an IP layer link to something at the other end. Connecting directly to the modem gives an IP via DHCP and I can ping the modem, but trying to reach the outside world fails. traceroute fails with the statically assigned external IP of the modem (which is stored in the modem's flash memory). LMI did not give us the admin password to the modem (grrr) and don't have 24/7 support. We attempted a factory reset, which reset _something_ since it lost memory of its external IP and the Internet light stopped coming on, but did not reset the admin password to the factory default (at least as specified in the manual). After an attempted factory reset again only one of the DSL lights came on. We then went to the box where the phone lines come into our building (in the phat beats room) and tied in a new, short, connection directly to the box and connected the modem. Again the same behaviour: Only the DSL1 line lit up.
As I write this email I'm realizing that since I didn't disconnect the existing phone cables running from the phone-line connection box in the phat beats room and to the server room, if that cable has been half-chewed over by critters then it might be creating a short which wouldn't be remedied by simply adding a new connection on top :/
I'll do another test where I untie the existing connection first. Assuming it still fails I will call our ISP tomorrow.
Will from the mesh group should have an unlimited 4G modem waiting for him in his PO box which he will lend to Omni after he comes home from work tomorrow and we will hook it up so we can have some amount of internet until it's all sorted out.