Sony VGN FZ21e battery problem

Hi my sony laptop is having some battery problems, basically I am only getting around 5-10mins of life from my two batteries. One of them is the origianl battery that came with it and the other is one extra one I had bought, also original from Sony. Before I buy another one I'd like to know if the problem might be from another source apart from the batteries themselves, such as the laptop having some problem which prevents the batteries from really charging up.

When inserted and left in the laptop the battery says 100% fully charged, but this goes down at an alarming rate when power is disconnected. I mostly leave my laptop on power as I dont move around with it much, and I recently heard that it is important to leave the laptop on battery so that the battery gets a chance to discharge through use then charge up again. I've not given it much occasion to do so so this could also have killed my battery, if this advice is true.

Your views are appreciated