Iphone 4 turns off with battery left?

My iphone shuts off with plenty of battery left. It only comes back on when i connect the charger. It turns on as if it had zero battery but when the home screen appears, the battery icon is at 70% (for example). If i disconnect the charger the phone dies again immediately.
When I try using the phone with the charger connected, I'm not connected to any network, i can't call anyone, visual voice isn't available.

Probably your battery is worn out and needs to be replaced. Most phone repair stores will put in a new one for about $30 or $40 - I think the Apple store will too.

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