Battery light stays on even after comp is turned off or the battery charger is unplugged

1. I try to turn on my computer after it goes into Stand By mode but it doesn't. The screen is off but there are 3 lights flashing to show its on. Its like only part of the computer is responding. 2. And then recently, I noticed that the battery light is still on when I unplug it and my computer is turned off or is in Stand By mode and the worst is the light is still on when the computer is off. Its not like its slow at responding and turns off the light later on, it stays on. I take the battery out and the computer is really hot even though its been off for an hour. 3. I've been getting a lot of those "blue screens" saying it can't reboot properly and it restarts but it doesn't progress. I just reimaged my computer and it just gave me the "blue screen" when I tried to use my computer. Is this an internal problem? Is it because I've been using an older battery charger at times? I checked the output voltages and they are the same. The new one is just lighter and smaller...