Iphone 3gs keeps turning off unexpectedly?

I've had this iphone for about 2 years and only recently this has started happening! Basically, I can turn it on, but it only works for a minute if i'm lucky, although, if I plug it into a charger, it stays on. I'm 15, i'm not constantly in my house and I need my phone for going out and about, people have suggested to me that if I update the current software on to my phone (witch is IOS 6.1.3) then this problem will be resolved, is this true?

Battery is dead! 2 years is typical for a battery life.

This is where you wish you'd bought a phone where the battery isn't sealed!

iPhones are not very environmentally friendly for this reason, but someone may be able to take it apart for you to put a new battery in, won't be cheap though.

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