first i would jack the front wheels off the floor (blocks under the mast with full tilt forward usually works)

then make sure the brakes are not applied (deadjust them if needed)
also make sure the parking brake is not applied (deadjust this also if needed)

if problem still exists then you have deeper issues as you suspect in the differential or transmission.

one other thought came to mind, you should pull the wheels and make sure all the brake hardware is intact, if any part comes loose and jams between the drum and any fixed part in the brake assembly it can lock up like this.