You do not need any special drivers to use the laptop's original built-in keyboard.
Did this problem exist before the reinstall? Why did you reinstall macOS? History & details are important as there is likely more going on here.
Did you perform a clean install of macOS by first erasing the whole physical drive before reinstalling macOS or did you just reinstall macOS over top of itself. If you performed a clean install of macOS, did you test the laptop before installing any third party apps and before migrating/restoring from a backup? If you did not, then you just left or brought back your original software issues.
Try booting into Safe Mode which should prevent the third party software from automatically running when booting the laptop.
Try running the Apple Hardware Test from one of the original DVDs which shipped with the laptop from the factory (should be on the second DVD).