It is possible that the float needle is leaking a little letting the carb flood when shutting off. After a few minutes, the gas may be evaporating to where it will start OR removing the air cleaner gives enough air to over come the slight flooding. You can pinch the fuel line closed if it does not have a fuel line shut off although a shut off is always good insurance unless the fuel tank is below the carb inlet. Walt Conner

Sounds to me like a battery or starter problem. Try putting a few drops of oil on the starter shaft where it exits the starter body at the top, make sure it can run down inside the bushing. Make sure all battery connections are clean, bright metal to metal. It would have been better if you had given the model number of the engine since there are several different 18 hp B&S engines. Walt Conner

Some folks can type messages on a computer, and some folks can start their tractors after a very long winter---but--never the twain shall meet! That said---better call the repair shop---you'll be neck high in grass by the time you get it to run! And, if you get it hooked up the way you asked about, the only thing that will run is you, as the garage lights up, and you run for the garden hose! Better seek close at hand professional help!

If the battery is more than 3 years old--buy a new one! Then, clean up all of the connections, such as ends of battery cables, and especially the ground wire where it bolts to ground, i.e.tractor frame, or body of tractor. Use new bolts, nuts, and lock washers to connect the new battery! This will make sure you have a good electrical connection in the starting circuit! there is also, usually, a fuse in the line somewhere. It will be one of those new style flat fuses, and easy to find. See if it has blown. You'll be able to tell easily. The little curved piece of metal in it should look to be in one piece. If it has blown, there will be a gap in it, and a burnt look. Also, the bolted connections to the starter solenoid are known to get corroded and cut off current to the starter solenoid! And, any battery cables with a green powder coming out of the covering are ripe for replacement. The seat switch wires should be connected, to avoid hurting anybody who might manage to tamper with the mower if you aren't on it! Especially little kids!