I have the "Power Saver" setting enabled, which is the default setting. According to the help file, when this setiting is on "Norton Internet Security detects when your computer is on battery power and suspends the background jobs. The background jobs include Norton-specific tasks, such as automatic virus definition updates, Norton Community Watch submissions, and Idle Time Scans. The background jobs resume when you start running your computer again on external power."
I hibernated my laptop (Windows XP SP3) while it was plugged in. I resumed from hibernation with it unplugged, so it was running on battery power. According to the Norton Tasks window, "Automatic LiveUpdate" ran 10 minutes after I resumed my laptop. About 15 minutes later "Idle Quickscan" ran. Both of these ran whiile the laptop was soley on battery power, despite the Norton Tasks window showing that they should only run when the laptop is on external power.
Pulse updates are not running, which is correct, so far Automatic LiveUpdate and Idle Quickscan have, which is wrong.
Here's a screen shot of Idle Quick Scan running while on battery power, despite the "plug" icon showing that it should only run on external power.
