I am trying to activate an application which sends my serial number to a server. The send is being blocked.
This is actually the place I'd start, as the term "blocked" is extremely vague. There are a huge range failure points for any network connection, most of which look exactly the same ("the connection failed"). The first step to this kind of investigation is figuring out exactly what happened, as that generally tells you what the solution is. The details of how to perform that kind of investigation can't be easily summarized, but here are some articles the might help:
Under what circumstances will Mac OS block outgoing internet connections from a non-sandboxed app?
In terms of what's part of the built in system, I can't think of any other cases beyond the one you listed. If the system did block something, it would have noted that in the system log (so you can check there) but my first guess would be that something else went wrong.
How else could the outgoing connection be blocked?
Again, this all depends on how closely you've investigated the failure and exactly what "failed". Strictly speaking, anything between your computer and the computer at the the other side of the connection can block the connection, however, the common failure points here are:
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Kevin Elliott
DTS Engineer, CoreOS/Hardware