TriggerFinger

First check your AC adapter (please say, this is not a universal adapter). Make sure the output ratings are correct. Original/genuine adapters show output voltage and ampere ratings. If you have a universal adapter make sure it matches exactly the said ratings. This is the safest way so far. Of course you can go higher (as the laptop will only use what it needs) but doing this may have some effects on the mobo circuitry eventually (heats up some components).

Now for the battery. Sometimes when I use an AC adapter with lower output power rating than what is required, the laptop still runs while plugged but battery charging seem to run ON and OFF. I noticed I cannot get the battery fully charged even after hours of charging. If I remove the AC, laptop will live for a minutes then die out due to no power.

I do hope you are using original/genuine battery. I noticed that some generics although they charge, they sometimes heat up in the process and does not go over 40%. These types also discharge twice as fast when used without AC.

May be what you can try is to use that battery on a similar laptop or try using a good/working/genuine battery from a friend's laptop of similar model. That way you can rule out battery or motherboard.