Toshiba Satellite power issue with AC adapter pluged in

My Toshiba laptop was working fine with the AC adapter plugged in (the battery was on it's last breath and would not charge at all, so I always had to keep it plugged it). I had to move so I unplugged the laptop (did not shut down). After the move I tried turning it on and it would not.

The AC Led light is on, so it's not the adapter.
The Battery light is amber and flickering (it wasn't flickering before)
When I press the power button to power up the laptop - the Power and the CD/DVD Led lights go on, but not the HD light. And the screen stays blank.
I hear no sounds, seems the HD is completely dormant.

There are a few files on the HD that I absolutely have to have. I'm not too concerned with getting the laptop to be operational, I just need to get those files and the laptop can be recycled.

Any ideas? How to get it to power up at least once, so I could copy the files?