I had this problem a couple of years ago on one White 13" Macbook, and now having that problem on my wife's. In both cases it made the trackpad and even this time use of an exernal keyboard and mouse inoperable, and so use of the computer with the battery in it impossible. In my case, after first being told at two different Apple stores that it was "normal" and my only recourse was to buy a new one, once I started to argue at the second store, the Genius Bar employee immediatly changed his tune and offered a free replacement.
I see that diuscssions of this problem go back as far as 2008, and yet it seems Apple has done little or nothing to solve this design flaw or to handle it consistently.
Is it "normal" for batteries to do this? My brother who works as an IT manager for a large nonprofit says he has never seen it hapen on a PC laptop. It seems, from what I can find, only "normal" for the Mac laptop battery. And to have a battery "normally" make your computer inoperable, seems to be to be a major design flaw that Apple should both take responsibility for and fix, irrespective of whether it is dangerous or not.