Dell Inspiron 6000- Battery and AC Adapter Issue

Hey,

I recently been having a problem with my Dell Inspiron 6000. I use this laptop for school and usually run on battery power. When I get home I plug in, and run on AC power. Yet, a couple of days ago when I got home and continued to work on my laptop I got a warning message that my battery power was running low. I found this odd and figures I mus have disconnected the AC cable from either the back of my laptop or my outlet. So I checked the connection and found that the laptop was still connected, so I proceeded to check the outlet. On the way to the outlet I checked the AC adapter and spotted that the LED light on the adapter was off, and I figured that the adapter had disconnected from the wall. But when I got to the outlet it was still plugged in. 

I then proceeded to disconnect the AC adapter from both my laptop and out let and reconnect them. I first plugged it into the wall and I saw the green LED light up. I then proceeded to plug it into the laptop and saw that the battery began to charge. But after about 15-20 seconds the AC adapter went off again. I tried unplugging and replugging everything and even changed outlets. I cleaned the contacts and made sure everything was plugged in tightly.

I then removed my battery from the laptop and tried just the AC adapter. I turned on the laptop and let it run. The AC adapter was working perfectly. I had no problems. So I then proceeded to plug in the battery to let it charge. Once again after 15-20 seconds the AC adapter turned off. So it seems that the laptop can run on either battery power or AC power but not while both are connected to the laptop.

So I have concluded that the battery is giving the AC adapter some problems. This provided a problem for me. While I can still use the laptop at home, I cannot charge my battery and thus can't use the laptop at school. The problem might be the battery and I might just need to get a new one, but the battery was still good when I last used it. Good battery life, stayed charged, when I check the indicator lights it lights up all green, so this leads me to think it might be more than just the battery.  I would get a new battery if that was all I needed but I'd hate to buy a new battery and then find out that it still has this problem.

Any advice out there?