I'm glad you brought up batteries. You have reminded me of an old Compaq Armada laptop that wouldn't turn on with the battery attached, no matter whether it was powered via AC or not. I think this was down either to a bad battery, or bad battery connectors on the laptop.
Try taking the battery off, and see if it works with AC
If you've had the battery off all this time, try putting it on and see if it charges.