Be careful about overcharging your battery though. I killed my laptop battery by keeping the battery attached to the laptop and the laptop was plugged into the outlet 24/7 for something like 9 month whether I was using the laptop or not.
That caused my battery life to drop from it's typical 5 hours to less than 10 minutes on a full charge. After several months of fully charging and full discharging the battery I managed to get it back up to about 2.5 hours on a full charge, or 50% of it's original capacity.
I don't see how this would matter, since laptops manage their own charging. My dell sits on either a dock at work or a charger at home all the time (Latitude E6510) so it's *always* charged. My battery still works fine when I take it off. You most likely have a faulty battery. You can't "overcharge" modern laptops. While periodic discharge cycles help a battery, the effect has been mitigated with modern battery technologies and has a very minimal impact. Leaving a laptop on AC power for extended periods of time has no negative effect on modern laptops / netbooks.