My iPhone 3GS won't stay on?

So since the weekend my iPhone turns itself off at less than 50% battery, then when I switch it back on again the apple logo appears but it will not go past that before it switches itself off again. The only way I can get it to stay on is if I charge it to 100%
However… Since last night it won't stay fully on even when it is plugged in to the charger in the wall (when I connect the USB to my laptop it is totally unresponsive) it keeps going on and off on its own. It now has 82% battery and will immediately turn off if disconnected from the charger.

Basically I'm wondering if there's anyone out there who can help me?

Added (1). Or you could read the question properly as I said, it keeps switching on and off even when connected to the charger.

Try charging it, Its not rocket science.

Change the battery.

Could be the battery the charger or the internal usb i have a 3gs but i'm using a nokia lumia now

I'm assuming you have had it several years at least as 3GS hardware is somewhat outdated now. You may want to restore it back, could be some app causing a problem. Another option is since iphone 4 is now free with a 2 year contract, just extend 2 years and get the 4 free as thats an upgrade on top of it.

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