This mower made an awful racket when it started from the top of the engine.  Right away I suspected the starter ratchet.  Usually you can get the top cap off of a B&S engine by taking off three bolts.  This is an unusual ratchet for a B&S engine (more typical for a Tecumseh) and when I disassembled it I found one of the pawls stuck out.  All it took was loosening the center screw and putting a little peg on the pawl back in a slot in the cap.

Usually B&S engines have a metal shaft with a ball bearing clutch on top of the flywheel.  The ball bearings often get stuck, or the shaft sticks to an inner shaft, particularly on engines that have been left outside.