Well, all of a sudden the shares on the TeraStation appear to be accessible from Windows again.
I ended up using FTP (from within Windows Explorer) to transfer a file to the device, and that worked fine.
An hour after doing that, I tried opening NAS Navigator, and the shares suddenly were accessible and the TS shows up in the Windows network.
The unit is also now accessible from other servers, and I'm able to copy via Windows Explorer.
Can't explain the cause, and don't know what made it start working again, but it does seem to be okay now.