Simply Put: My iPhone's acting crazy. Help!

I just purchased an iPhone yesterday, and I'm already having problems with it. It was working fine earlier today, but for the past hour it's been acting weird. I'll turn on iPhone with Home button, slide to unlock it, and then one of two things will happen: 1. After 5 seconds it turns off, or 2. It works fine. If it goes with option 1, I can't turn it back on. If I press the Home button, it will take forever to finally turn on. The same is true if I press the Sleep/Wake button. When it does finally turn on, it sometimes will freeze at the unlock screen, and I have to wait for it to finally just shut itself off. If I get option 2, where it works fine, if I try to go to Mail, it won't show any of my mail messages, freeze, and then go back to the home screen. I reset my iPhone, deleted my email account, and re-registered the account, and tried again, but it continued to do the same thing. Oh, and another problem is sometimes when I turn it on and unlock it, it will only show the signal bars, ATT, time, and battery meter at the top, but nothing else, and then after about 30 seconds to a minute the home screen will finally appear.

Does anyone know what is wrong here, and how I can fix it? This is very upsetting to me that I am already having problems with it after just buying it yesterday.

Thanks in advance.