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My battery came to an end after 5 years almost so I bought a new one on ebay from a good seller. I’ve put it on charge and it charged fine after an hour perhaps. And when I tried booting it, the mac doesn’t respond. When I touch the button on the side all green lights apear, so the battery is ok I guess. I tried resetting the SMC, didn’t work eitheri tried ctrl command and power button, didn’t work either. Anyone have any idea what can I do?

Here’s the IFIXIT guide you’ll need to follow: MacBook Pro 13" Unibody Mid 2010 Logic Board Replacement. It’s not overly difficult if you can handle small fragile parts.