I called 1&1 again and they said that they had received (and processed?) the cancellation of my existing ADSL connection from T-Com, and the lady I talked to looked at the state of the line and said that there was a port free, so they could proceed to ask for a new connection. She said that it would take ten to fourteen days for them to receive a connection date from T-Com, which they would then communicate to me in writing. So with luck, I should have Internet again by the end of March, maybe quicker (depending on how long it'll be from the time that T-Com notifies 1&1 of the connection date and when the date actually is).
Also, happy birthday jAna!