I have just tried a further experiment with the modem attached to another computer and then to the laptop, watching the two LEDs on the modem (OH - Off Hook - and Data.
When I queried the modem from within Device manager, there was no difference, either to the lights or to the recorded result.
When I tried dialling, however (without a cord connected), the "other" computer lit up the OH light for a short while. However, this did not happen with the laptop. The OH light stayed off.