Briggs and stratton 18hp motor won't start, soleniod clicks - starter motor engages flywheel but barely turns motor - now won't, even when shorted with car battery. Starter will spin strongly and freely when off motor

Set valves clearance

DG is probably right. If the valves are out of adjustment it will have too much compression and keep the motor from turning over. More than likely this is the problem.

Have you removed the spark plugs to make sure that there isn't gas in the cylinders? If the carb is faulty it can leak gas through it and will fill up the cylinder and keep it from turning over too. It is easy to check. Just take out the plug and try to crank it over with the plug out. Make sure you tie the spark plug wire away from the cylinder when you so this. If it spits out gas this is your problem. If not then the valves are probably the issue.

Lastly, the starter could still be the issue. Even though it cranks freely off the motor doesn't mean that it isn't worn out and not able to turn the motor by itself. But my bet is on the valves... Just giving you some more info.