Q: Why won't my iPhone charge?

Today as I was using my iPhone, the battery started to drain really quickly. It went from about 20% battery to 3% battery in less than a minute, and I didn't have any applications running other than my messages. I plugged it in but it would not charge past 5% and the percentage charged kept dropping to 1%. I turned it off and when I tried to turn it back on it displayed the red low battery meter. It's been on that screen for almost 2 hours now and I can't reset the phone or turn it off. I held down the power button for 30 seconds and nothing happened. I tried again by holding down the power and home buttons, again for 30 seconds, and still nothing happened. How do I fix this? This is the first time I've had battery problems, and I've had the phone for less than a week. There is nothing on the phone that is dangerous, illegal, or very draining to the battery, and I am sure it wouldn't have any virus. So what is wrong and how do I fix it?

Thanks.