Is this damaged MacBook worth fixing?

I recently bought a 15inch MacBook off a college friend and it's broken, it doesn't power on without the charger and it does not hold a charge when plugged along with another operating issue. I bought it for dirt cheap, how and where can I repair it? Would apple repair it even though I'm not the original owner? It doesnt have a service plan. Thanks
The battery is an issue but it has operation issues I'm not familar with macs. Should I go to the apple store?

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