I asked a question that involved a system that has now been wiped, as troubleshooting was taking too long, so no further answers can contribute to the question, as it was specific to that system. That said, there were a lot of good answers, and so it could help someone else should they search come across a similar issue.
EDIT: Here's the question I asked: Dell M6600: "No internet access", can browse internet, can remote into it, cannot activate office 2013, cannot join domain