SQL Server, SSMS, and IIS all running on the same machine.
This is an inherited project, which also happens to be my only experience with DNN. It turns out, it wasn't a database connection issue, despite what the error indicating that it was. So whoever is in charge of error messages, might want to dig in to see what other scenarios the error might show up.
I was able to get past the issue by downloading the latest version (it was 2.1.1 I believe), and doing an upgrade. Since the upgrade succeeded, that tells me the real issue wasn't connecting to the database. I then had to dig into the database to see how DNN handles URLs, because I was getting nothing but 404s. Making some updates to the PrortalAlias and related tables, I was back on track, only to find I'm missing some Skin/Container files.
So it looks like for now, I'm in a good spot, and I believe should be good until I receive missing files. DNN error messages could still use some work to more accurately portray what's going on.