(We get free phone calls on Sundays but only to "normal" numbers, not service numbers, which most Internet connections use. But some ISPs also have normal numbers and they make money from the interconnection charges that our phone company pays them for the connection.)
Also, I guess that the dialing program leaks memory when connecting over and over again -- at any rate, some of the fonts were gone and the system said it didn't have enough memory to start new processes.
I finally dialled in with the number I use during the week and checked a web site which lists some publicly accessible local numbers. Tried a bunch of them but kept getting "No-one answers", until I finally hit one that worked (which I'm using now). Well, at least I'm in now, but I'm still a bit annoyed that it took so long.