iphone 3GS: Can it be fixed with a new batt?

Hi

I have a very old iphone 3GS - I think maybe 6 years old and now it is quite clearly dying a slow death. I cannot use it for calls as it crashes immediately after, the battery life is totally unreliable - it will die when it says it has 50% or more, or, when I've charged it, the battery will drop to a low number very quickly, and it always crashes when I use apps. Basically, it's useless.
My question is, could it be salvaged with a new battery or, after 6 years, if the actual computer hardware going to be coming to the end of it's life? Is it time just to get anew phone?

Thanks