ColdFusion 9 suddenly won't consume Web Services...

Ok, the weirdest problem has cropped up, and I'm hoping someone will have a solution...

Suddenly none of the Web Services we're consuming will work from our production server...

Our test-server, locally-hosted, will consume all these web-services just fine.  But when we try to consume the very same web-services on our production server, it'll just hang forever.  No time-out, no error of any kind; just hangs there forever...

We do not publish these web-services, we're just consuming them...  These web-services are being published by several different companies (our clients), so it's not that they're all coming from one source and it's the source that has the problem...  Every last web-service we consume has suddenly quit working when we try to access them from our production server...

So why would we be able to consume them on one server, but not on another?  I've gone through the ColdFusion administrator line-by-line and both the test-server and the production-server are set up precisely the same way...  The only difference between the two servers is the OS and the fact that the production server is quite a bit more powerful...  Test server: 2-core AMD CPU, 4GB RAM, Windows 2003, IIS6,  ColdFusion 9;  Production server: 4-core Intel Xeon CPU, 8GB RAM, Windows Server 2008, IIS 7, ColdFusion 9...

I'm really confused about this -- it's almost like the production server has had all outgoing requests blocked somehow...  But even if we completely turn off the firewall, we still can't consume any Web Services...

Has anyone had a problem remotely like this?  I'd appreciate any kind of help you can offer...

Thanks,