Possible that the battery is bad or weak, the adaptor is not outputing the required voltage or is faulty or that the charging circuit is faulty in the motherboard.
In all these you need to check on the voltage incident on the battery terminals. So connect the adaptor an check the voltage at the battery terminals in the laptop, if absent check at the pins, if absent check on the adaptor circuit.
check this link;
http://www.fixya.com/support/r5164850-laptop_power_supply
If voltage is present then the battery is a suspect, if not the motherboard charging circuit has problems if adaptor is good and there is no charging.
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