I think I am right (perhaps other forum members would verify) in saying that it is impossible for a hacker to control your PC while it is turned off!
If all your USB modem's lights are OFF then it means that no data can flow in or out of your PC even if the computer is on.
I normally do this by using XP's 'Safely remove hardware' option on the taskbar.
I do this when I want to disable the anti-virus as with some programs (like TRS 2004) it is recommended to disable anti-virus when installing the application.
I think what it means by an 'always on connection' is that you don't have to dial up your ISP as you had to do with a 56k modem as the broadband data is already digital (not analogue i.e. sound) hence the description 'DIGITAL subscriber line'.