Don't have many snow blowers here in Vegas but based on the occasional unit we see from up on the hill, here's my take.

Prime it two or three pushes. Pull out the choke all the way. Turn on/off key to on and crank it. In the shop I immediatly push the choke all the way off but in actual operational cold conditions you may need to push choke only to half off for a minute or so.

@nevada_walrus
Thank you for the advice. I realize two cycle engines vary for the amount of primer pushes required.
Just didn't want to flood it on the initial attempt.

In the shop where ambient temps are certainly higher then how a snowblower is actually operated I prime them 3 times. They may require more under actual operating temps but honestly I doubt it.

These things have no air filter as is normal with snowblowers. The main nozzle which the prime squirts out of is in the center of the venturi, the narrow part of the throat, At least half the prime shot rolls down the inlet side of the venturi. By the third if not 2nd prime fuel is dribbling out the inlet. Thus by the third prime, half of the prime shot is dribbling on the ground. So after the 2nd prime, it takes two prime shots to keep the fuel of one prime in the throat. So I kinda gotta believe the manufacture doesn't feel more then 3 shots is needed as anymore will dump half on the ground. It also makes over priming more difficult then an arrangement that would keep all the fuel in the throat.

@nevada_walrus
Appreciate the follow up.
I think what I'll try is two pushes of the primer, if that doesn't work I'll give it a third.

I delivered it to his house so I can't really toy with it, also the weather has not been that cold for the true test since it is being stored outdoors under a tarp.

I can only say this, after the carb rebuild I pushed the primer about 4 times and it started on about the 4th pull.
After running awhile, I tweaked the carb settings, it then started immediately on the first pull. The real test will be how easy it starts when it's cold.

In my experience it is pretty hard to flood a 2-stroke to the point it wont start. My experience is if you over-prime or flood it, it will attempt to run for a short, smoky time. A few more pulls clears them out, and away they go.

I am trying to find out if a regular extension cord can be used with a S620 1988 Toro Electric Start Snowblower, or if you must purchase a special cord from Toro

To WLF1: If the female end of the cord fits the prongs on the starter area--yes--it will work! 110 is 110! 110 in--110 out!

I have a toro s-200 and have had it tuned up and fixed three times at 65 a pop and tired of it. I have cleaned out float and carb already and it ran until i ran gas out of it and now put in gas and wont start again what to do. what to do and we just got hit with alot of snow and a shovel aint cutting it.

Toro s-200 starts, cuts off when I turn the
Choke back. Also, do you really need to
mix gas and oil?

yes you must mix oil with gas for all 2 stroke engines on yard equipment. This provides the lubrication for cylinder/piston and
bearings on crankshaft. You will sieze the engine otherwise...not good !!!!!!!