Tecumseh 8hp 1978Craftsmsn Snowblower

I'll take a look at an old snowblower. Maybe I can find out something about your kill switch wire. A photo would help.
 
In any case, since you say you have spark, your problem is not the kill switch. Whatever its wiring is, its not the reason your motor won't start. Look instead to the carburetor as being the most likely cause. Junk inside the bowl is probably clogging up the jets. But before you start tearing the carburetor apart, let's just bypass the carburetor by spraying some starter fluid down the carburetor throat and then trying to start the engine.
1. Open the choke (normally you would close the choke to start a cold engine, but not when you use starter fluid; a choke increases the fuel-to-air ratio by cutting down the air; starter fluid increases it by adding fuel).
2. Stick the nozzle of the starter fluid can down the throat of the carburetor, and give it a 1-second shot. Too little won't work, and too much will wet the spark plug. Start with 1-second.
3. Pull the cord.
4. If the engine starts and runs for a few seconds, you've proven that the carburetor isn't providing fuel.
5. If it doesn't start, but you see a few puffs of smoke come out the muffler, or if you heard the motor sort of cough, the motor was on its way to starting, but probably didn't have enough starter fluid. Try again with a little more, but don't go crazy since you'll wet the plug and then the engine won't start until the starter fluid evaporates.
 
Let me know what happens. Maybe we can then go on to the carburetor cleaning phase.
 

SRTsFZ6
 
Varnish built up from sitting with un-treated fuel:

 
Agree if you do indeed have spark it's not an electrical problem! And if you have a carb that looks like SRT's above you need some serious cleaning. Even if it looks clean I would flush out all passages with carb cleaner. I know my small engines can have problems at the start of season no matter how good they look. Often takes a tank or two of fresh gas before they don't have a little rough running problem.