I had the same problem that my iphone 4 appeared charged then just suddenly quit. No screen picture. Nothing. Zilch.
I followed all the good advice about various hard resets like pushing the on button and home at the same time, then holding the home while I plugged it in to the computer with itunes running. All to no avail. The screen was just dead.
I called Apple repair and their advice was to buy a new phone as the old one (probablay only 3 years old) ws not repairable. Not good!
The next day repeated pressing of the on button brought up a screen picture of a battery and charger symbols. So there was life after all.
I looked at the youtube videos for opening up the phone and decided that it was not too difficult.
I bought a toolkit and a new battery. I followed the instructions, replaced the battery, then put it all back together.
I pressed the on button and low and behold the apple logo appeared in the screen. It took ages to load the operating system and I was beginning to despair when the home screen appeared. Everything works and the phone is as good as new after a proper charge.
Analysis of problem
I am not sure that this was just a failed battery. It was too sudden. Batteries die slowly.
My theory is that the device got in to a serious sotware loop or suffered a memory malfunction which stalled it. The so called hard reset buttons were not really strong enough to properly restart the device. I am sure that they dont for instance wipe the RAM ready for a reload.
Only disconnecting the battery thereby fully stopping the device was sufficient. Hence the very long reload time after the new battery was connected.
I could have tried to re use the old battery but I was not keen on messing about and felt that while the device was open a new battery would be worthwhile.
I would be very interested to hear from a really knowledgeable apple technician who would be prepared to talk honestly. There seems to be a bit of a conspiracy to say that the phone is not repairable and that a new one is needed.
I hope that this helps to encourage others to take the plunge and at least disconnect and replace the battery.