Just because this thing cost me more troubleshooting hours than I'd dare admit, I'll post the solution to my problem... just in case it can help someone in the future.
Here are the symptoms:
- After restoring it, my Surface Pro 3 could not connect to my Synology DS215j NAS anymore (via the Windows Explorer, \192.168.1.2 in the address bar).
- Pings were going through
- The WebAdmin was responding all right
- I could access the file tree via my Phone (DS-File app on Windows-Phone 8.1)
- Both machines are in the WORKGROUP group
... but I could not browse the files via the Windows Explorer.
The solution was dead-easy (isn't it always?): I noticed the "Client for Microsoft-Networks" was missing from the Ethernet adapter settings (Network and Sharing center > Adapter > Settings). Installed it:
Cover Image: Cory Doctorow CC BY-SA 2.0