After you put the new hard drive in did you get it formatted? Can you see the new hard drive? Will it start from the CD? Put the old hard drive back in and see if the problem is gone. What drive did you put in? What color is the light on the AC adapter? This should not happen, so try removing the RAM and reseat just one at a time since that's the only compartment you were in, right? Did you open anything but the battery compartment?
The first course of action is to ensure that everything is correctly plugged in to both sides of any cable that involve the left I/O board.
I would guess there is a bigger issue due to the machine running fine off battery power, but it's always good to remove any variables.
The next step would be to try a different adapter.
The next step unfortunately would be to replace the left I/O board.
Good luck! Keep us posted.