Problem solved.
Turns out it had NOTHING to do with my ISP or my Firewall or DNS.
We deployed a web-filtering product called Untangle.
It's an opensource program that allows me to block specific websites, ports, services, etc.
(For example, block 'myspace.com' from employees)
Apparently there was an update to the Untangle definitions which caused this whole mess. (There's lots of talk about it on the untangle forum)
In any case the issue was resolved and now everything works again.
Thanks to all for your help, though ... it was very informative!