What font are you using? Not all the fonts have the necessary code points mapped in. The default Notepad font, Lucida Console, definitely does. And IIRC, the NT6.1 version of Consolas does as well (but not the NT6.0 version, at least for some of the ranges). And, IIRC, Courier New does too (though it's been a while since I checked). Many other fonts (esp. those not supplied by Windows), however, do not.
It's also possible, though unlikely, that you somehow uninstalled/deleted your Asian fonts. The fonts mentioned above don't actually contain the characters, but rather, they contain tables that "link" to the actual Asian fonts.
It's also possible that Notepad is using the wrong code page to open the files, though given your symptoms, this is highly unlikely (since this would normally manifest itself as a different kind of nonsense, not the "appear as rectangles" type).
It's also possible that some program somehow overwrote those fonts mentioned above with an older version that lacks the proper mappings for the Asian code points, though this is also unlikely because the Windows system file protection mechanism should've prevented that.