Dell 620 Battery Issues

I have a Dell 620 office machine. It's on AC power all day, and I noticed it yday that in the evening when I take off the AC power, it shows low battery.
And even after taking it off the AC power, it shows AC Power icon on the right hand side bottom taskbar. Checked the Power options in control panel. Everything seems to be fine.
Took out the battery (kept it out for a minute) and then placed it back in. Did not solve the problem.
So, now whenever I take the AC power chord out- it goes low battery.
& even after taking the power chord out , the icon for AC power doesn't go off.

Please Help!