Is there a chance that you burned up the starter by cranking it too long trying to start the motor when you had no spark? In other words, is it possible that you had no spark before you burned up the starter?
If you may have lost the spark before you worked on the starter, then you could have a bad ignition module or a bad coil. Your 1992 engine probably has an electronic ignition module, but some early models of that engine had points and condenser which could also cause lack of spark, especially a bad condenser. Mis-adjusted breaker points could cause a weak spark.
If you are sure you had spark before you worked on the starter, then here are two possibilities:
(1) You accidentally pinched the primary wire from the coil to the kill switch causing it to be grounded to the frame of the machine.
(2) The spark for that engine is created when a magnet built into the flywheel passes by a U-shaped armature/coil. You can find those if you remove the engine shroud (the tin covering over the engine, usually held on with three machine screws on a Briggs engine).
If the machine was sitting for a little while when you were fixing the starter, there may have been some rust build up on the flywheel magnet and/or coil (armature).
The gap between the flywheel and the coil is typically about 0.010 inches (about two thicknesses of typing paper). A little rust on either the coil or the flywheel magnet can kill your spark.
Use sandpaper or emery cloth to remove the rust. You can adjust the gap by (1) loosening the two screws that hold the armature, (2) pulling it back from the flywheel, (3) turning the flywheel so the magnets are next to the armature, (4) placing an index card or two thicknesses of typing paper between the armature and the flywheel, (5) letting the armature stick to the flywheel magnets with the index card in between, (6) tightening the two screws, and (7) removing the index card.
You can download a parts list (exploded view) of your engine here:
Manuals | Customer Support | Briggs & Stratton