Note that the ground terminal may "possibly" be completed by a safety switch. There's multiple ways that safety switched can be implemented and it's not as straight forward as one tends to assume. If you have a meter, ground the neg lead and measure for V from the small wire that comes from the ign. switch in the crank position. IF you have V, then try jumping the "other" small terminal to ground and see what happens when you hit the key. Have you checked the fuse yet? Sears parts site is down at this time, so I can't check the switch number, but it's NOT an MTD. Make sure you have the correct part if you're going to go ahead and replace it.

The fact that the plug shows a "whitish" color, AND you have intermittent "popping back through the intake", AND that you can "somewhat smooth out the running" by partially closing the choke, all confirm that there is not enough fuel reaching the engine. The plungers do sometimes get gummed up and reluctant to open fully (and sometimes, not at all). You can try removing the fuel solenoid and soaking the plunger tip in a small container of spray carb cleaner. Fill the cap from the can with cleaner and stand the solenoid on its tip in the cleaner filled cap. Prop it up so it can't fall over. Soak it like this for a few minutes then push the plunger into the solenoid body a few times. The plunger should have a slight resistance or spring pressure when pushing it in. It should pop back out when you quit pushing it in. Repeat the soaking and manual moving of the plunger a few times until it operates freely. You can "bench test" the solenoid by using a 12VDC source (the tractor battery will do) by connecting the body of the solenoid to the negative pole of power source and the wire lead of the solenoid to the positive pole of the 12VDC source. The solenoid plunger should retract into the solenoid body when 12VDC is applied, and pop out when the current is taken away. You might have to push in ever so slightly to get the plunger to retract because in some cases, the plunger will be sticking further out of the body with the solenoid removed from the carb than when it is installed. This is because the design calls for the spring to actually PUSH the plunger valve against its seat with a bit of spring pressure. If the plunger does not "jump into" the solenoid body as soon as you apply 12VDC to it, just give the plunger a little nudge to get the plunger close enough to the electromagnetic field for it to "grab hold of" the plunger. The plunger should remain retracted for as long as the 12VDC is applied. While you are into this carb, check to make sure that the main jet is not partially clogged or varnished up. It is also essential that you have a good, free flowing air filter in place as well. While in this case it appears that your engine is "starving for fuel", you must remember that the fuel is "drawn out of the bowl by venturi effect". If you do not have good FLOW (which equates to induction air velocity) through the air filter, the venturi effect will be weak and so will the volume of fuel. Another thing you want to make certain that the cooling shrouding and fins have not been converted to a mouse haven over winter. These critters will carry all sorts of stuff in to create their condo. This can completely block the air flow from the fan. Overheating will also create a "lean burn" condition (just before everything siezes up).

I would first Check the pre-filter, if its dirty clean it and knock any dirt you can get out of the paper filter. pull the spark plug, check the gap, clean it and reinstall it. You may want to change the paper filter if alot of dirt come out. Next buy you a can of carb. cleaner. follow the instructions on the can to clean you carb as david suggested. If that don't help then it you will probably have to take the carb off, apart and clean the small passages inside the carb. Most likely it's just gummed up some from setting over the winter months and following the instructions on the can of spray carb cleaner usually will ungum it. Hence the name gumout! All of the above is annual routine maintance and the older the engine gets the more often you have to do it.

Does it die if you have the transmission in neutral and take your foot off the brake, or only when it is in forward or reverse? If it dies in neutral as well, then it is probably a problem in the seat switch (Operator Presence sensing) Might be a good idea to check all safety interlock switches on the machine to make certain none have become disconnected. Also post the LT Model nomber from your owners manual or the data sticker somewhere on the machine.