For no particular reason, it connected this morning and registered the device after a few plug-ins and out. So, there's hope for the rest of you! Thanks, Quinn!

Nice to know I'm not going nuts! Or: have some weird firewall blocking issue, although the fact that Chrome makes it through would count that out!

The appleid trick is not working for me; I just get the same waiting icon.

I can't get to developer.apple.com either, via Safari, because to log in there, it goes through idmsa.apple.com , which again can't load the header.js and app.js and app.css resources.