That requires me to determine why my "Turn Windows features on or off" list is blank, of which there's a variety of possible causes/solutions and it's not the common ones. :(

(Or locate a third-party client, but a quick check of the options didn't uncover anything acceptable; everyone recommends the Microsoft one.)

Sounds like hell has just frozen over.

Doesn't Windows assign a 169 address when it can't actually get a "good" address from DHCP?  I think you really need to use a different IP range.

Another thing, did you say you're using a wireless adapter for internet and a wired adapter to only access the NAS?  If that's the case, I've had times where the adapters come up in the wrong order and one doesn't work.  I would disable the wireless adapter and try to access the NAS.  What happens is Windows looks for the NAS over the wireless adapter and of course it won't find it there.