Battery on the fritz! Help!

So I've researched this problem in other forums and websites, and I think I've diagnosed it correctly, I just want to make sure before I have to go to Apple and get another battery.

Background:
I fully drained my battery a couple days ago, to the point where it shut down and would not turn back on until i had left it plugged in for about 15 minutes. For the next 2 days, everything was fine; i used my macbook in class and the battery drained normally. Yesterday I went to use my macbook on battery, and after i unplugged it, it told me I had 10 hours of battery life. I thought nothing of it until that number didnt change as I used it, and then shut down on me without warning. After plugging it back in at home, I noticed the battery charge indicator read "Battery Not Charging". I unplugged it to see why it wasn't, and it shut down on me. I restarted it and browsed through a couple forums and webpages trying to figure out the problem.

This morning I started up my computer after shutting it down last night (I had installed the latest safari update before shutting down), and everything appeared to be normal. The indicator read "Battery Charged", and when i unplugged my notebook, it said "Calculating...", So i thought everything was good.... until it told me I had 10 hours of battery life left I unplugged and replugged it several times, hoping it was just a glitch, but it wasn't. I accidentally left it unplugged for too long, and it shut down on me, so I had to write this whole thing again.

I've read that other people are having this problem as well, and that the battery's defective and to get a new one, but I don't understand why it told me it was "charging" this morning, and it wasn't last night.

Any ideas/suggestions? Or have I hit the nail on the head? I tried to be as specific as possible, in hopes that someone will tell me that I don't have to get a new battery. I don't have Apple Care, but it IS still under the 1 year manufacturer's warranty. Does that mean I still get it for free? I don't have the money to buy a new battery.

My Macbook isn't that old; purchased brand new in March 2008 from Apple.

thanks guys!

Since it is under warranty, there should be no problem getting the battery replaced (if that is what the problem is). Take the computer, AC adapter and battery with you so that the Apple folks can check everything.

I do definitely suggest that you scrape up the money to get AppleCare before the 1-year warranty runs out; one repair can easily run way more than the AppleCare cost, so you are definitely living dangerously not having it.