Well, depending on average daily hours of usage and usage pattern, which is what silverpersian is alluding to, two years may be the life expectancy for a laptop battery.
The fact that your computer says the battery is fully charged is misleading; that doesn't necessarily mean the battery is still capable of running the computer. I have 3 year old Compaq laptop for which I still have the original battery, and I have a fairly new battery I bought about 6 months ago, as I recall. The old battery (will computer unplugged) will still run the computer but will only run it for about 16 minutes, starting from a "100%" charge. The newer battery will, of course, run the computer much longer from a full charge.
So, what you're seeing is basically 100% of near-zero capacity. Does that make sense?
Tip on where to buy a battery: I bought mine from Amazon.com for only about $30. Be sure to get one that's right for your model computer.
Edit: by the way, you can extend the life of your battery by leaving it out part of the time and running directly off power from a wall outlet. But, don't leave it out for weeks at a time.