That engine has 2 coils, they are independent of one another. Seeing spark jump the gap of a spark plug OUTSIDE of the combustion chamber does not prove there is a spark when the plug is threaded into the head. Compression changes the operating parameters enough to "blow out" a spark sometimes when a magnetron (Briggs coil) is defective. Swap the coils to the opposite cylinders and see if the problem follows the coil to the other cylinder. You will have to physically dismount and move the coils, you can't simply swap plug wires (if they would even reach). This would beat just buying a new Magnetron (as Brigg$ is $o proud of them).

You didn't say how long you ran these after you ran them out of gas??? IMO and from experience running my V-twin out of gas it takes awhile to get all the air out from the tank through the hoses through the fuel pump, then from the fuel pump to the carb. and into the carb. fuel bowl itself. these weak vacuum pumps on Let's have a hard time pulling fuel up when air is trapped in the system IMO. I would remove the hose at the inlet side of the pump lower it and let some fuel drain so all the air is out from that side. you can prime the other side of the fuel pump by pouring fuel down the hose. Or just start it up and run the thing at full throttle, it will go up and down till all the air is out of the fuel lines, pump, and carb. bowl. sometimes moving the throttle up and down works the air out quicker and some times it don't matter till all the air is out of the fuel delivery. another trick is to remove the air cleaner and start it up and use carb. cleaner to keep the thing running till all the air is worked out. this also cleans the carb. some while your trying to get the thing to run right. I ran my out of gas maybe 5 times in 18 years and every time I had to fiddle with it to get it running right. Check the gas before you run the machine will help and knowing how long your machine will run on a tank of gas prevents this from happening, By what you described that is nothing wrong with these mowers other than air trapped in the system. You've got to keep them running long enough time it get worked out.

I do have an ohm meter! i will check the switch they gave me. im questioning if they even gave me the right switch?? again if i disconnect the grounding wire to the coil the engine starts and runs great! so im assuming that the safety switches are good?? i DONT HAVE A SCHEMATIC of the mower wish i could find one online somwhere for the tractor. i will check the terminals on the switch tonight and get back to you.. how do i test the safety switches exactly? the seat switch i put a jumper wire in and it did nothing.... the clutch switch is a 4 wire switch and there is another one for the deck that is a 4 wire. which i assume keeps the mower from starting if its engauged. not sure how to test the 4 wire switches.. thanks again for the help

In this case the elect. fuel shut-off solenoid (item 1) in in place of and older design carb. that just has a bolt to hold the float bowl on. Just remove the wire and using a wrench on the hex portion of the solenoid. This solenoid will click and open when you turn the key to the on position moving the plunger that mowie talked about to let fuel into the carb. you can test this by simply removing it ground it out against the carb. (with the power wire connected)(or you can use a battery charger with the + connected to the elect. hook-up and the - grounded against the body of the solonoid) and turn the switch to the on position. you should see the plunger actuate out when power is supplied (12V) and retract when power (12Vs is removed) Other than that spraying the passages and seeing if float works is the same as older design carb. remember their will be two gaskets when you remove the float bowl, 1 on the solenoid to seal it against the carb. bowl(usually a crush type gasket that can be reused if it didn't get torn up during removal, 2 o-ring at the top of the fuel bowl which usually sticks to the carb. housing and can be reused if it didn't get damaged during removal. you want the o-ring on the carb. housing for installation and not on the bowl cause the bowl slips over the o-ring and will most likely get pinched if put inside the bowl when installing or have it on the carb. housing to alow the bowl to slip over the o-ring for a good seal job, but you still have to look and see if it's pinched out while tighen the solenoid. as with all o-ring installations you need some type of lubricant to ensure you don't pinch the o-ring when installing it, most use small amount of vasoline jelly. If you have pinched it fuel will leak when the float fills the bowl up. To prevent pinching of the o-ring install the bowl and hold it up against the carb while screwing the solenoid on hand tight, now look around the bowl where it meets the carb housing for the o-ring sticking out, if you don't see no protrusion the tighten the solenoid using a wrench on the hex part of the solenoid. Tighten as tight as it was coming off trying not to over tighten it so you don't smash the crush gasket on the solenoid creating leak. most people with general knowledge and do this, if you have fuel leak try to see if the fuel is coming from the bottom or the top of the fuel bowl? remove the bowl inspect the gaskets and try to reseal it again, if it still leaks then you will have to take it to a mechanic which IMO will cost you no more that taking in as long as you didn't lose or damage parts during the trial maintenance repair. kinda of long sorry.