This mower made an awful racket when it started from the top of the engine and spit out the starter rope.!  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 the normal ball bearing starter for a B&S engine:

Often on engines that are left outside the starter ratchet freezes up and the rope will not retract, or is very slow to retract - same problem.
To access the starter, you remove the two small screws and the screen.  Don't forget to put them back on when you reassemble it - I always do!

Now you can pop off the cap covering the works.

The works look like this.  Six ball bearings, each in a slot and five teeth on the center spinner.  The center spinner will pull straight up off of the inner shaft, pull it and the ball bearings.

Here's the parts.  Now polish the center shaft (I use steel wool) and clean up everything.  Lube everything (especially the inside of the spinner and the center shaft).  I use spray white grease, but a heavy oil would work too.

Now put it back together. Spinner, balls, cap, screen and screws.  You probably had to disconnect the throttle cable when you took the engine cover off, so pay attention to getting it back together with the throttle working right!  Should be good for another five or ten years now.