It did show my network in the list, so I told it to connect. It thought about things for a few moments, then declared that the password I had entered was incorrect or invalid. Now, I've not touched my network setup for a while now so whatever password it had saved should have worked, but again apparently not. So I dug out the passphrase, entered it in, hit submit... and after a few moments it decided that not only was the password invalid, but my wireless network no longer existed either. And no matter how much I pounded refresh, it was now convinced that my network was a figment of my imagination.
Funnily enough, the computer that I'm typing this post on works perfectly well using that non-existent network.
Eventually I got it to connect, after switching airplane mode on and off several times in the hope that this would actually make the wifi module start behaving.