My Iphone 4 has 'no service' and turns off by itself?

Basically my iPhone 4 just turns off by itself and the only way to turn it on it so plug it into a charger but when it turns on it says 'no service' but I don't know whether that is to do with a new sim I got. Because I lost my phone and blocked the sim then I got it back and had to register another one with the same number but it doesn't seem to give me any signal so I'm not sure about that one.
Also when my phone decides to turn on it says that WiFi is unavailable so I can't connect to any internet. I sometimes have to do a network reset but that doesn't always work.

So basically I'm just wondering whether i need to get a whole new phone or just replace the battery?

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