OK, all that leads me to believe that you may (and I emphasize may) have a hardware fault, somewhere in the wifi card area. At this point, since you can't wire the PLAYBASE directly to your router with an ethernet cable (which would be the only way to ensure that knowledge, as far as I know), I think your best bet is to call directly in to Sonos and speak to one of their reps.
The interesting thing is that the other speakers are showing up. It might be because you did a factory reset, but generally those speakers are "bonded" to the PLAYBASE, and communicate with it on the 5Ghz channel. But the factory reset may have broken that "bond", leaving the names intact, and put them on your normal wifi channel.
Give Sonos a call, and see what they say. Sorry that I don't have any rabbits to pull out of my hat.
Bruce