MBP trackpad not working, but Apple (store) got it to work during reinstallation of macOS
Reinstalling OS X will keep your previous system preferences set up.

Trackpad could be disabled in the System Preferences Accessibility.
Since in your case you had the Logitech plugged in, the system just did what it was asked and disabled the trackpad.


  USB Receiver: Product ID: 0xc52f Vendor ID: 0x046d (Logitech Inc.)
  Version: 30.00 Speed: Up to 12 Mb/sec Manufacturer: Logitech Location
  ID: 0x14200000 / 14 Current Available (mA): 500 Current Required (mA):
  98 Extra Operating Current (mA): 0




Solution: Disable the check mark in the system preferences Accessibility.