Hi archeologist,
I saw your post regarding the problems with the notebook freezing while on battery power and while browsing Firefox. I would suggest that you are start by testing and calibrating the battery. You mentioned you are using Windows Home Premium but not if you are using XP or 7. I have included a couple of different links below for you.
Testing and Calibrating the Battery Windows 7
Checking the Status of the Battery Windows XP
Thank you,