Can I still be infected with virus this way?

I’m using a cable modem for my internet and couple days ago I had a connection problem
The light indicators on my modem are

All of them except for standby should be on when the connection is active. However couple days ago the PC/Activity light wasn’t turned on at all. Vista was reporting that I had the cable unplugged and I had no IP and no internet connection. I let the modem turned on all day long though.

The Power, receive, Send and Online lights were all turned on.
Could a virus infect me while the PC/Activity is not turned on?
The cable was plugged alright until this day I don’t really understand why the PC/Activity light wasn’t turned on. The call center and technician also didn’t quite offer any good explanation.