Ages since I used a modem for internet access so just a couple of thoughts.
Can you see the modem and is it enabled in Device Manager? Go to Control Panel - System and Security - System then Device Manager link. Should show the modem. Right-click for Properties.
I am somewhat surprised that it detects the presence of a connection when the cable is or isn't plugged in. Modems are pretty dumb devices so not sure I would expect it to detect anyway. Yes I would expect it to report a disconnection on an ethernet connection but a modem? Like I said, a long time since I used one.
Preciso.so you plug a cable into your laptop and the cable modem and you don't get internet?
The laptop should report whether a cable has been plugged in or not.