I just got a msg on my laptop that my battery isn't charging, despite the fact that it's been plugged in for hours. It's only about a year old. Do batteries just die like that. Sorry for the ignorance, but I'm more of a desktop guy.
Damaged power port is a pretty common problem with laptop. You can try fiddling with the power cord when it is plugged in. Might be able to get you going for a while before you can it it repair/replaced.
Does the port have a lot of play when you connect the power cord to it?
Like Jimbo said, Battery tend to lose longevity before they become unusable. I would also suspect a bad connection on the mobo adapter.
If you used the battery a lot it's possible that it's already finish. If your laptop is on warranty take it in the shop so it can be check. Before spending $$ on a new battery. If not I would open the machine carefully ( I found guide whit google for my HP ) and check the power connector. There could be a small crack in the board or one of the pins came lose. It's fixable but it require good finger skill and proper tools. If you see no problem whit the connector. Then I would move to the battery. Try to find a replacement on ebay for cheap. So that if the battery is not the problem then you did'nt spend much $$ on it.
I used my HP laptop battery a lot and it took about 1 year 1/2 before I lost 1/3 of it's power life. It lasted 3 hours and I used to empty the battery every day and it slowly drop to 2 hours, then 6 to 8 month after it gave me only 1 hour.