Why will my laptop only work with power source when battery is 100%?

I have a Dell laptop that works perfect when it is plugged into a power source but when unplugged, even though the battery is at 100%, the laptop will go completely dead with no power at all. Someone recommended looking at bios but there is a password needed and I dont have it. Is there any way around this or will I need to buy a new battery?

Additional; When I click the power button, it shows 'Battery One 100% - Battery Two Not Present' not sure if that means anything.