Thanks for the suggestions.
It was easiest just to delete the saved passwords from the keychain, but that didn't work. So, I tried changing the SSID on the router, and unfortunately that didn't work either. Finally, I just turned SSID broadcast back on, and now it's automatically logging in when I boot the computer. I'm pretty sure that it used to find the network and log in with SSID broadcast disabled, back when I originally bought the router, but maybe some recent system update broke it.
