Poor battery conditions, iPhone performances limited?

Hello everybody,

big question on an iphone 4s white 16gb EU.

The battery pin is not in good condition and the iphone works only when plugged in and sometimes it turn off by itself ---> battery problem right?

But it has other many problems, like no speaker, no microphone recording, no alarm clock ringing etc...

This iphone is in very good condition, intern and extern is looking as new!!!! Why this troubles are happen?

Is it possible that the poor battery condition influences other performances of the iphone? Or this are simply defected parts?

Thanks guys for your suggestions