I couldn't figure out how to check the battery level on the Acer. There's an Acer User Guide (and a Quick Guide) in PDF accessed through All Programs from the Windows Start button. The User Guide said there was a battery icon on the taskbar. (At this point the computer was still plugged into the wall.) There was no icon, but there was an AC icon in the form of a plug that said "On AC Power". The minute I unplugged the computer from the wall, the plug icon was replaced with a battery icon. Voila! This is not so mysterious.
Now that it's unplugged, it goes right into standby mode when not in use for a minute or so.
I'm glad I got the 10" netbook. My fingers just fit over the keys, with no room to spare. (I can see myself building up some speed eventually.)
Now that the battery icon dilemma has been solved, I can relax. Everything is working as it's supposed to (so far). Knock on wood. I downloaded the Firefox right away, before the malware could start creeping in. (I downloaded it the minute I plugged the Ethernet cable into the netbook--right as Internet Explorer was welcoming me and telling me how great it was). And the anti-virus program was up and running at that point.