Thanks for the info, and I'll see about giving that a shot. One thing I want to make sure I understand - the Perl SOAP requests are done via LWP's to the https://vc_server_name/sdk/vimService url, so the only port I should be worrying about is 443, right? I can use a web browser and go to https://vc_server_name without issue (the web access link, for example, uses that), so again this seems to me to point to a VC issue, not a network issue.
One other thing - I downloaded VMWare's OVF appliance and loaded it on to one of the hosts controlled by the VC that's not working. I tested the VIPerl code on that appliance and it failed with the message "SOAP request error - possibly a protocol issue: 500 SSL Read Timeout". The SSL Read Timeout is curious. Again, it seems to me the only port that should matter in this discussion is port 443 since these are (as far as I can tell) vanilla requests sent over SSL. That error message made me wonder whether the webservice isn't listening on the right port, but again, port 443 seems to work fine for the web access. And then I also have to keep in mind that the API seems to be fine when queried locally (from the VC itself - when I go to https://vc_server_name/mob, I can see the managed objects just fine, and presumably it is querying the API for that).
Incidentally, I did a netstat on the VC, and the results are:
TCP 0.0.0.0:80 0.0.0.0:0 LISTENING
TCP 0.0.0.0:135 0.0.0.0:0 LISTENING
TCP 0.0.0.0:443 0.0.0.0:0 LISTENING
TCP 0.0.0.0:445 0.0.0.0:0 LISTENING
TCP 0.0.0.0:735 0.0.0.0:0 LISTENING
TCP 0.0.0.0:1025 0.0.0.0:0 LISTENING
TCP 0.0.0.0:1493 0.0.0.0:0 LISTENING
TCP 0.0.0.0:2967 0.0.0.0:0 LISTENING
TCP 0.0.0.0:3389 0.0.0.0:0 LISTENING
TCP 0.0.0.0:8009 0.0.0.0:0 LISTENING
TCP 0.0.0.0:8086 0.0.0.0:0 LISTENING
TCP 0.0.0.0:9084 0.0.0.0:0 LISTENING
TCP 0.0.0.0:9086 0.0.0.0:0 LISTENING
TCP 0.0.0.0:27000 0.0.0.0:0 LISTENING
TCP 0.0.0.0:27010 0.0.0.0:0 LISTENING
TCP :2381 0.0.0.0:0 LISTENING
TCP 127.0.0.1:2301 0.0.0.0:0 LISTENING
TCP 127.0.0.1:2381 0.0.0.0:0 LISTENING
TCP 127.0.0.1:8005 0.0.0.0:0 LISTENING
TCP 127.0.0.1:8084 0.0.0.0:0 LISTENING
TCP 127.0.0.1:8085 0.0.0.0:0 LISTENING
TCP 127.0.0.1:8089 0.0.0.0:0 LISTENING
TCP 127.0.0.1:9085 0.0.0.0:0 LISTENING
I compared it to one of the working VC's and nothing jumped out at me as being wrong.
So basically I'm just a whole bunch of confused. I really don't know where to go from this point. If I can get a packet tracer going I will, but not sure if I'll be able to.
Good times.