Sean,
I have not yet found a cause or fix, but my suspicions and time spent looking at this lead me to the following:
1. It is a combination of old(er) hardware, an old Windows 7 image, and Avast.
2. The more I look at it, search online, investigate, and troubleshoot personally, it looks more and more like some sort of software firewalling.
Some computers act as if they have no connection whatsoever. Others have some limited network services, but cannot reach beyond our network. This is pretty frustrating.
Thanks,
Ryan