Laptop always says it's on AC Power

I'm not very technical or good with computers, just to preface this.  My laptop is a latitude d620 and I have just recently (about a day or two) noticed that when I unplug my computer from ac power, it says that it is still on AC power.  The red battery light will stay on when I unplug the computer.  Sorry if this has been asked already, but is this simply something like I need a new battery or charger, or something more serious.  Thanks!