I've spent a lot of time with Blizzard support working on this (GOG redirects to them for Bnet issues), they're at a loss as well.

This is the error message I'm getting:

https://i.imgur.com/DqF7yL0.png

Ports are forwarded. I've rebooted into a launch of Win10 Pro 64-bit that had almost all startup apps disabled (so only essential MS services + internet), then I tried connecting and still got the same error. Game has been uninstalled and reinstalled, is on the latest version. Win10 has been uninstalled and reinstalled.

Ideas?

Do you have updates enabled? Microsoft broke Windows 10 (even more) time to time. Do you install DirectX 9.0c update (full redist or Web installer)? If Web installer say that no files need to updates, go to Control Panel Installed Windows components - Enabled Windows components - Enable Legacy DirectPlay.
Turn off Windows Firewall and any other Firewall/antiviruss programs.

this erro rI got when i havent got network, you got antivirus or firewall? maybe it block if you didnt allow it?