A few days later, one could not reach me over my landline any more, although I had to pay for further two months. I didn't mind, since I did hardly used it anyway and did not complain. However, when the landline service finally and officially run out, the email account was blocked immediately too.
On the same day, I went to their webpage, and filled the appropriate form to complain. I got an acknowledgement of receipt and since then absolutely nada.
By the way, it took Swisscom more than three weeks to swap my mobile service to 3G.
To look a bit on the bright side of my Swisscom experience, this is the landline hardware I got rid of:
