After making the post above, my iPad began to work again for no discernible reason until April 2014. It failed again, and nothing seemed to cure the problem. As a last resort, I upgraded my imac from Snow Leopard (10.6.8) to Mavericks (10.9.2). This allowed me to upgrade to a WPA2 password on the iMac's wifi (Snow Leopard only used insecure WEP passwords). My iPad then asked me for the new password, and the wifi began to work.
So in this case the 169 problem seemed to be caused by the wifi's old WEP security system (and yes, I was using the correct password).
I'm glad my iPad is now working again. I'm not glad that I had to waste three days of my time to get it working.
For the record, you can set a WPA2 password on your iMac (if you have upgraded to Mavericks) by going to System Preferences > Sharing. Untick 'internet sharing'; highlight wifi and click on wi-fi options.