Lo and behold, after downgrading to v1.0 and re-upgrading to v1.4 Wi-Fi works -- I really didn't expect this to have any effect.
It's still an odd issue, though, or even more so considering the way it appears to have been remedied.
Now only the battery issue remains; I guess I'll exercise patience and see whether a discharge-charge cycle results in the device charging to more than 84%.