Two possible causes: bad AC adapter or bad battery.
Try different AC adapter to see it will charge the battery.
Do you use the AC adapter plugged in all the time? If yes, it is charging the battery all the time and killing it. It will not hold the charge any more. Battery is supposed to be fully charged and fully discharged. Happened to me and cost me $250 to replace battery. Only use the battery on the go.
Sorry but thats very bad advice....
It used to apply years ago to NICAD batteries but with Lithium batteries it destroys them if you charge and then fully discharge them (deep cycle)
With Litium batteries you leave them plugged in ALL the time when not using the lappy mobile...
All the best Brett