Question about computer batteries? Please help?

HI this is my first time owning a laptop of my own. I've had it since last summer, but now, it had just shut down and it tells me that the battery needs to be replaced. I am currently charging the computer so that I could use it.
If I change the battery, would the computer be like it's brand new again? Or would the faulty battery damage the computer itself?
I'm really worried. I always hoped that I could keep this laptop for a long time.
Thanks to all :)
 
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