Laptop With Windows 7 Won't Shutdown With/without Cord

I have an HP Laptop model 6735b with an AMD Turion DualCore ZM-84 Mobile processor and 2GB of RAM. I purchased it in January 2009 and installed windows XP on it, which I had no problems with. I recently installed Windows 7 on it, and it will not power down or go into hibernate mode without being on external power. When I tell it to hibernate or shut down it will power the screen down, but thats as far as it will go without being plugged in. All of the lights stay on (volume control buttons, wifi indicator, etc.), the hard drive continues to run, and it will stay like this until I plug it in, at which point it will finish its power-down or hibernation.