Just for info, I switched the WiFi on today and it seemed to go a bit crazy. Turned out that there was a software update taking place.

Yep, these things happen. Mine updated on Monday.

Is there another update happening? My Paperwhite has gone crazy again.

Edit: It finally came back to life after doing a couple of restarts all of its own. I then checked the software version and it was 2 out of date (5.3.6 instead of 5.3.8) and so I have forced an update. It is still doing it.