You can probably find more info on the Lawn & Garden Tractor forum. There's a link to get you there. Here is a link that might be useful: Ariens vs. Troybilt vs. Craftsman Lawn Tractor

I realized in my initial thread I wrote after the fuel pump when I meant to say after the fuel FILTER. This engine is model 274844. So a fuel line goes from the fuel filter (the original fuel line comes from the fuel tank under the seat, to the fuel filter) into this round black plastic device, and a vac line goes down from this part into the area where the valve cover is, and another fuel line exits this and goes to the engine. So three lines total, 2 fuel one vacuum. The part just says "ikuni" and "made in japan". I'm sure you're right about bad diaphragm in fuel pump. Where to find the part?

Engine Model & Type numbers are always handy so we know exactly which engine you have. Without looking at the engine, it's hard to know exactly what "blown" means. It might be as minor as a "blown" head gasket (not uncommon) or very major damage to the internal parts. Why not ask the "mechanic"? You pretty much have to remove the head to reinstall the valve keepers. Not a major job if you have some mechanical aptitude. You could probably do it without the valve spring compressor if you have strong fingers and a 3rd hand. You can down load a pdf IPL from Briggs at the link below. BTW, on Briggs OHV engines, the valve lash is checked with the piston 1/4" PAST TDC. I can't speak for Sears how they would deal with the situation. You might ask them or Briggs, since it is an engine issue. Here is a link that might be useful: Link

"No start condition" - is that a $10 phrase for "The $@#& mower won't start"? :) You might have better luck posting this question in the Lawn Mowers section, or the Tool Shed. I'm no expert, but if you're getting backfiring, I'd say that the ignition must be firing, but the ignition timing is so far off that the plug fires when a valve is open. I guess it could also be valve timing. I don't know what drives the camshaft in small engines these days. I guess a lot of them have OHV now. That's a long way from the flathead engines I hacked at in my reformative years. Haven't owned a gas mower in 30 years. Ignition timing still seems to me like the most likely reason. Again, I'm not a small engine tech, just a long-time tinkerer.