Ignore Dan the 2010 MBP has okay graphics and an okay cpu and while it’s definitely slower in catalina and runs much better on 8gb it’s fine on 4 for lighter use. Install the app drivedx and see if it points to any issues you may have a faulty hard drive cable or resistors that have failed on the data line causing slow transfers. you may also have an SMC issue where it’s telling the cpu to run slowly If you remove the hard drive cable on this there’s a tiny black SMD choke right next to the logic board connector that’s easy to flick off with your nail, don’t do that it’s a nightmare to solder back on.
If you’ve changed the keyboard and the fault is still there then the issue is clearly the logic board and that should have been obvious. You’re issue is likely the keyboard connector pins are bent and needs a new connector soldering(very delicate work) or liquid damage corrosion to a joint or probe point which can be fixed with enamelled jumper wire.
I’ve just been fixing one of these tonight if theres no light on the charge wire and you’re sure the charger is good its likely a blown u7000 but its worth changing q7030 and q7031 while you’re here. I replaced a u7000 tonight the tools I used are a MUSTOOL G1200, 858d hot air ‘station’ max heat and low air, soldering iron with 900m-t-s bent tips, leaded solder and fine tips on my multimeter. I have experience with bits of hot air soldering and its at the limit of my abilities and very easy to create a dry joint. I appreciate this is a long and complex answer but I’d prefer the information to be here for the next guy so they dont get told to repeatedly reset the smc.