Check the battery and see if has a self test button, if it does what is the status?
Try the AC adapter without the battery, will it power up?
Is the jack for the AC adapter a bit loose? These DC jacks can get broken loose from the motherboard, sometimes you can wiggle the plug a bit and the system will power on.
If the AC adapter is 2 piece, you can disconnect the cord from the brick, then unplug and reseat the cord in case it was loose.
Try another outlet, or try another device in that outlet.
Otherwise, you will need to get the AC adapter tested, or have the power system checked out.