my phone keeps shutting off without it being dead. And when i try to turn it back on it shows the apple symbol and goes black and doesnt turn on. I have to Plug it up to the charger just for it to turn on and it has the same batteryy life before it died. Why is it doing this? and what can i do to fix it?
It sounds as if the battery is getting old and is either close to being consumed or is failing. This happens in time as the chemical's useful life expires.
If you want to keep your 3GS (rather than upgrade etc) then book an appointment for the Genius bar. They can run diagnostics on the device and if it is the battery at fault, offer you a replacement 3GS at the cost of a battery (rather than the cost of a whole phone).