Jim, I'm having problems following your posts and visualizing what the issue is. You bounce back and forth with the engine 'not turning over'. That would mean it is not rotating when the key is turned. Then you state you 'have spark' or 'does not start'. This would mean that it is turning over, but not firing or starting..
I would check for compression first. Remove the spark plug and insulate the spark plug wire. Lightly put your finger in the cylinder plug hole and crank the engine. You should feel good size puffs of air forcing your finger out. Not an accurate test, but will indicate some compression. If compression is there, you could squirt a small amount of gas, or cleaner, directly into the cylinder. Replace the plug with a new one. Crank it and see what happens. If it does try and run, squirt more gas or cleaner into the carb intake. See if it continues.
If it won't run, then I would think not enough compression or leaking out the head gasket or valves. I wouldn't think timing as you said the key was already replaced. Most of the Briggs have the kill wire on the bottom of the coil and the coils orientation is stamped on the laminated metal. Removing the kill wire will eliminate safety's from being an issue. If you do get lucky and it starts, you'll have to choke it or pull the plug wire to stop the engine. Best of hunting.