It may be due to the battery. I have a Dell Inspiron 9400 and it has a sony battery and dell and a few other big laptop names have issued warning about the sony batteries and have asked to take it back to where you bought it and check because it could burst into flames at any moment: http://news.bbc.co.uk/1/hi/business/5390948.st m
Are you sure it's fully charged? The only way to check is by using a voltmeter. Chargers are notorious for falsely indicating a full charge, since many simply work on timers. It may be that the battery needs to go through several charge/discharge cycles before it's really fully charged, especially true of NiCads.
It's hard to discharge it if it's not actually powering the machine ! I've tried two different batteries that work in other machines, but this laptop just doesn't seem to like batteries !