Laptop turns off when i remove the charger!

Hello,

I have a Advent Roma Laptop which i bough from a guy from a internet site, only for me to find out that the laptop has a battery problem. Everytime i turn it on it gets to the point of "starting windows" then suddenly it just bleeps off and shuts it self down, this also happens when i remove the charger when i am surfing the web it would be on 56% for example and would turn off without the charger plugged in, Help