What's a reputable laptop battery seller?

My laptop has been unable to power on (even when plugged in) and when it does power on after cycling through on and off (never see the screen turn on tho) it might randomly shut down or, in one instance, plugging in an external mouse caused it to go black in the screen.

So first, I assume battery since I used this for around 4 or 5 years now without replacing a battery, but is this what others would conclude? Second what seller to buy from who isn't amazon?

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