Found troubleshooting steps; they don't work
A tech support page says we should "Open My Computer and navigate to the Install folder inside the Battlefront folder on your harddrive. The default install location is:
C:\Program Files\LucasArts\Star Wars Battlefront\Install
Double-click the CDKey.exe file and reenter your CD Key printed on the sticker on the back of your Battlefront CD Jewel case
Now try joining a multiplayer game once more to see if the problem has been corrected."
I did this. No change. They also suggest, on the same page, that a used copy cannot be expected to work online, because the previous owner may have registered it [which I think is a silly excuse, but it doesn't matter in this case, because mine was a sealed, new copy].