Step one:
:itcrowd:
Step two:
CHECK THE SETTINGS. ALL OF THEM.
It was around 2am when I got pissed off with tech support and the tech did some basic tests... and that's when I discovered that the DNS settings on the appliance were set incorrectly. Two minutes later, I put in the right DNS and we fixed that problem.
Then we checked the firewall, and I'm sad to say that I can't use the "It's Not the Firewall" image. Waiting for the outsourcer that manages that firewall to get around to permitting DNS to the IP address that makes all this work.
:wall: :doh: :angry: