I agree with Joe: it is routine to check the aluminium key that locks the flywheel to the crankshaft, since they are prone to shearing if the mower suddenly jams in a big way. This is fairly common on rotary mowers though I think less so on reel type mowers. Since it is not the carburetor or fuel system, and it is not the muffler, the only possibilities left are loss of compression, or ignition timing. The ignition timing will be correct if the flywheel key is intact, so after checking the key, you need to check the valves. Before removing the cylinder head you should check the compression. Briggs and Stratton recommend you do this by rotating the flywheel backwards (not forwards) until you feel compression, then move the flywheel slightly forward, and flip it backward against the compression. If it bounces back, the compression is OK. If it doesn't, you have either a ring-sealing problem or a valve sealing problem. However if rotating the flywheel backward does not indicate any compression at all, you have a stuck valve, very badly blow head gasket, badly burned valve, broken piston or connecting rod, or something along those lines. You can conveniently do the B&S compression test while you have the air cowl off to check the flywheel key. Remember, though, disconnect the spark plug lead first.
If there is no compression at all, you need to remove the cylinder head and take a look at the valves and piston. If there is compression but it fails the B&S test, do another test before you remove the cylinder head. Remove the spark plug, put about a spoonful of engine oil through the plug hole, reinstall the plug, and either repeat the B&S compression test or operate the pull starter to see whether the compression has improved markedly. If it has, your piston rings are shot.
