Macbook Pro doesn't switch on unless I take off its battery (mid 2010)
Li-ion batteries do not respond well to being allowed to run absolutely flat. If they drop below approx 2% power, a firmware switch will kick in & not allow then to be recharged.
A professional may be able to circumvent this, but it is potentially hazardous & should not be attempted by the user.
Your choices are…
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Leave it on charge for another day & see if it's actually charging, albeit slowly.
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Take it to a repair shop & see if they can 'reboot' the battery.
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If it will run without the battery, then try that. It will throttle down & will probably crash hard if you stress the CPU or GPU, as the charger alone is not powerful enough to run the computer under high load - that's what the battery is for.
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..of course… buy a new battery.