So your laptop will only run when it is plugged in and will not run on battery is this right?
Then no matter how much charge the battery indicator is 'saying' it has, your battery is probably done for and needs replacing.
As they go, they hold less and less of a charge. Due to this, they can say they are at 100% when they are really only holding 10 or even 5% of a normal charge.
If the device is still under warranty, contact the manufacturer about a replacement battery. If not, then I suggest you go with an OEM battery and not an after market one. Even though after market stuff is great for a lot of things, it isn't for laptop batteries.