Hard Drive Always Running Even When Turned Off

I noticed lately that my battery would always go dead after I shut off my Acer one. I thought it was the battery so I swapped it with my Wife’s. I had the same problem with her battery and my original battery worked just fine in hers.
Today I noticed that there was a slight noise coming from my computer after I shut it down so I put my ear against the back and heard the hard drive still running. I took out the battery and the hard drive stopped. I then put the battery back in and the hard drive started back up without powering up the computer.
I tried to find other people with the same problem with no luck.
I hope someone reads this that can tell me what is going on so I don't have to pull the battery every time I put my computer away.
Any help will be greatly appreciated.

UPDATE: I flashed and updated the bios and now I get the black screen of death! I tried to flash it again but nothing happens except the hard drive is running like before. I ended up taking the computer apart and removing the bios battery and re flashed it. It worked again but took the battery out to save the power and its giving me the black screen of death again.
Please Help!!!