IPhone – Run iPhone with network off, wifi on

Have you tried testing the connection coming straight from the modem? The only good way to really test this is by connecting a computer directly to the modem over ethernet and seeing what kind of connection you have.

Does Airplay work for you? If so, another reason why I think there's nothing wrong with the router. Have you done a hard restart of your modem. Try that first as it's the resist thing to do.

So if I understand it correctly, it's not available in your LAN, cannot directly connect to a computer using USB, is unable to make a bluetooth connection and cannot connect via the cellular network either? Is there any interface that is working, other than the touchscreen?

Do you have any experience with opening up iPhones? It is not particularly difficult if you're careful and precise, and excellent guides can be found on ifixit.com. If you have another iPhone available (that is no longer under waranty, as opening it up voids that), you could consider 'borrowing' one of the interfaces from the other phone. If you have the parts available, I recommend attempting to replace the WiFi antenna.

Alternatively, you could attempt to insert another battery and hope it lives off the donor long enough to connect via usb without needing the wall charge.

Either way, as you say it's water damage, it could do wonders to open it up and let it dry or acitvely dry it yourself - bowls of rice have done miracles. This strongly depends on how long it's been since bathing time.