"Verification failed" for AppleID on new iPad Pro

Trying to configure a new iPad Pro, but it won't accept my AppleID and password. I keep getting "Verification failed -- There was an error connecting to the Apple ID server."

I've tried rebooting. Logging out on my iPhone and website. The username and password is correct, but it won't work on the new iPad.

It's online and otherwise working .. but I can't get access to my apps or download any new ones.

Help!