Hi, the screen didn't refresh or something and I just saw the two replies above.
Meanwhile I did the whole remove-the-battery-uninstall-ACPI-Control-Method-battery thing, now it's still beeping madly but so far is continuing to charge. Odd thing - I installed BatteryBar and the icon in the toolbar shows me roughly how long till a full charge is reached - but every time it beeps, the time remaining estimate drops by half an hour, then a second later the time-remaining image changes to saying "A/C" as if it briefly doesn't recognize that a battery is even installed. The A/C message goes away after a couple seconds.
At any rate I'll try the above suggestions. No I didn't charge with laptop turned off - sounds like a good rule of thumb with any computer!