Why my iphone 3GS turn off when bettery is 50% of below and could not turn on back on

S

Sothy

macrumors newbie
Why my iphone 3GS turn off when battery is 50% of below and could not turn on back on, by pres sleep + home button even when i try to connect to computer. But when i charge it turn on then i try to disconnect from the charger at 50% of battery it off again. so what is the problem with it?
 
Jailbroken, all ios version.
i've tried ios 5.0, 5.1, 5.1.1, 6.1.3. still the same problem.
 
sorry, i've no idea about the age of my iphone because my relation give it to me. but actually i got this problem when i change my touch screen. mean that before my touch screen is broken it work very well but after that i got this problem. is it problem when i change the screen it could effect to the battery or not?
( i didn't done it by my self.)
Thank you for reply.
 
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