Steam Client Won't Connect.

Using the Linux build, I was attempting to play Team Fortress 2 on Saturday, which I have done successfully before, and it wouldn't get past Parsing game info, so I closed Steam deleted the config folder and restarted it. Afterward I had to re-verify my Steam account with Steam Guard, as expected, but after typing in my code I get told "Failed to contact Steam servers The Steam servers could not be contacted at this time. Please try again later."
I have tried several times since including just now.
I also tried Windows and it wouldn't connect. I deleted all of the stuff, except steam.exe & SteamApps, as recommend on a troubleshooting page. Afterward, it updates, I have to verify, and it ends the same way as the Linux installation.

Some notes:
I have a 10Mbps connection; nothing else is using bandwidth.
My computer is connected directly to my router.
There is no active firewall.
It seems to all coincide with the latest update on both.

I sent a message to Steam Support on Sunday, but they are slow. Have any of you had similar problems? Any resolutions?