Well technically the battery can come out and be replaced. It just may be a real pain to get to.
Try charging the laptop when it is turned off and see if it will charge. Then see if it will turn on when not plugged in, if it does charge when turned off.
If it won't charge when turned off, then you probably need a new charger. If it won't turn on with the battery only (even if it says it was charged) then you need a new battery.
If it gives you both issues, then you probably need to replace both.
NOTE: If the device is still under warranty to do not open it up to do the battery replacement yourself. Contact the manufacturer.