Constant shutdown and loss of data (by 2 users)

When it's in the cradle or pluged into the power suply it will run fine but when i take it out it stays on for a few seconds then turns off. Some times it will come back on and just sit on the boot screen and then i can't turn it off. The battery if fine as it registers as full when it is put back in the cradle and will stay on for ages on the boot screen.