G came back quite early for lunch and so he volunteered to phone the carrier again. He was assured that the package was on the van and that it would arrive after lunch.
And despite my bad feeling that it wasn't going to come and I still wouldn't have my broadband upstairs, the package did actually arrive. So the broadband is now accessible on the laptop in my study. Hurrah!
But I can now confirm that G's old desktop computer has no network card. The thing that I thought might be the socket for plugging in an Ethernet cable turned out not to be for that purpose. This means that my desktop machine probably doesn't have one either, though as getting to the back of it is a major operation, I haven't definitely confirmed that yet.
So it will be a few more days before absolutely all the computers have broadband, but I am now far more confident that we will get there eventually.
Meanwhile, it is sooo nice to be able to use the Internet as much as I like at any time of the night or day, without having to think, "Is it the off-peak time when I don't have to pay by the minute?" Also, even on the laptop which is far less powerful than G's new computer, it's delightfully fast.