That is weird.
It sounds like you might have a hardware issue.
So all it does is turn on, then off and restart and so on?
Yes, that is very weird
Here this is what going on to the phone:
>>
If the phone is NOT plug into the PC and it is On:When I press and hold the Power button for few seconds:The screen go black, but there was no "slide bar" for me to slide to turn the phone off, so I assumed it off because it went totally black; when the phone is off (it only a guessed) if I press and hold the Power button for about 4 to 5 seconds the Apple logo appeared for about 2 seconds then the USB cable and the iTune logo took place, and for about 30 seconds more the screen went black, if I press the home button, nothing happen !! (I assumed that the phone is turning itself off )

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When the phone IS off : It turning itself on right after i plugged it into the PC (the USB cable and the iTune logo appeared on the screen)
>> When the phone IS plugged into the PC: When I press and hold the Power button for few seconds the screen will go black but as soon i release the Power button, the phone turned right back on and of course, the USB cable and the iTune logo again...
>>
When the phone continuously plugged into the PC: It's cycling on then off, on then off, on then off.....it's doing it in about every 10 minutes or so !!!!
It has been this way for about 2 weeks now, I just don't know what to do. I am very fustrating right now ... Some one please help me !!!!!