After the fact, it turns out their DNS servers were down. I was finally instructed by the Xbox Live tech (who was very good) to turn my console’s DNS settings from automatic to manual, with these settings:
PRIMARY DNS: 8.8.8.8
SECONDARY DNS: 8.8.4.4
I’m no computer geek and and I know many of us aren’t either. Apparently DNS is basically the ‘phone book’ for web addresses. We type in a website address, DNS pulls the actual numerical website address. With the DNS servers down for Time Warner, there was no way for our consoles to “find” the proper sites, including Xbox.com and Account.Live.Com, etc. SO - everything is back to normal NOW, and I’ve put my consoles’ DNS settings back on automatic. But for future reference, you might want to print this out because TWC isn’t going to tell you “Hey, our servers are down.”
Hope this helps someone.