Q: iphone 4 turns off randomly with battery remaining

Hi ,

My iphone 4 has been switching off randomly even when battery is 100% and wont switch back on unless connected to a power source.

This behavior is more prominent when  i connect to 3G or when i turn on or turn off the flight mode.

I have already changed my battery and also restore my phone to factory settings with latest ios update but still its not working as before.

I do not remember dropping my phone or it getting in water.