Well, that clearly shows it isn't a Windows issue. That leaves the router or the disk itself. My guess is the router; like you I think the disk is just a passive device without this kind of intelligence.
So it might be time to try another router. For a test, there's no need to connect it to your modem or to Internet. Just turn off the modem, turn on the router, maybe reset the wired connection (ipconfig /reset), find the wireless in your PC/laptop and see if it sees the NAS.