Problem Turning the iPhone 3G On

Question

I think this started two days ago when my iPhone ran out of batteries for the first time since I got it in September.
I charged it overnight and it began to work normally again. Yesterday I was using an application (NY Times application) on the phone and it just turned itself off. I turned it back on, went back to using the application and it turned itself off again, so I thought the problem was the application. I turned it back on and used Safari and again the iPhone just turned off. After this time when I pressed the On button the apple would show as if the phone was starting up and then it would turn off again. After doing this three times or so the apple stopped showing. I put the phone to charge even though it had almost full batteries and it started showing the apple again, but it turned itself off afterwards.
I left it at the charger and in two or three hours I went to get the phone and it turned on normally. While using it later at night to check my email, the phone turned itself off again, and afterwards the apple startup appeared before the phone once again turned off. I went back to the charger left it there and the apple startup appeared and the phone turned itself off again. Then it wouldn't do anything when I held the On button. I went to bed thinking that leaving it to charge would do the trick.
This morning the phone won't respond to anything, nor the charger, nor the computer, nor the On button. I have no idea what's wrong with it because it's in perfect condition, and it's always worked perfectly.
What should and what could I do?
Thanks in Advance!
Luiz P

Answer 1

Standard troubleshooting is
1) Reset (hold sleep/wake & home button until the Apple logo appears)
2) Restore (connect to iTunes and click the restore option)
If 1 and 2 do not work, the next step is to take it into the shop to be looked at.