Question about cable modem?

Having been on dial-up for years (my internet needs are relatively uncomplicated by today's standards) I am finally surfing quite a lot faster via my local cable company who made an offer I couldn't refuse. I have a Motorola SURFboard SB5101 modem provided by them, and my question is about the "PC Activity" indicator light. The modem is always on, of course, so I expect the indicators for "Power", "Receive", "Send" and "Online" to remain glowing even when my computer is turned off. I also understand that when the computer is up and running, you are always online, even if you don't specifically have your browser open for surfing; the PC Activity light flickers rapidly on and off in a random pattern, which is also understandable and looks quite normal to me. What I'm wondering is why, when I shut down the computer (not standby or hibernate, it's shut completely down), the PC Activity light continues to flicker away exactly like when the computer is running. Since the computer is turned off, there's no electrical power going into the computer, so there should be no activity to register on the modem. At least that's how I see it, and I admit up front that I don't know much about broadband.