Help with Craftman 5.o snowblower model @ 536885211

Is this a gasoline welder? I'm afraid w/o being able to look at it, I can't tell much? Is the fuel a gravity feed to the carb or do you have a fuel pump? Is there a fuel filter involved? Does the carb have a float? If so, does the float bowl have gas in it? I don't know if they have a carb kit for this, do you think it would help?

Well if the pump works then follow the pump fuel lines to the engine,you will find the fuel filter then replace it and will also see petrol if any in it ,if not pump isent working ,if dirty replace it and blow air back from carby to filter to clean out pipe
,turn on ign fuel should come to filter and then with new filter in turn on fuel and see if any comes to carby if ok it should start and run.
Have a goodday,

Sounds like gummed carb, you may have to pull apart and clean the jets.

Your carb needs cleaning. It's probably old gas that has gunked the jets/orifices. Remove the carb and clean it out.
What tells you it's the carb is that you can get it to run by getting gas into the engine.

Check air filter. Try to run without filter. If not, add gas through carb and see if she'll fire. If she does,
clean the jet

A big problem you have is the gas leaking from the carb. This means your float that allows the right amount of gas in the bowl for everything to run right is either stuck or the float itself is leaking (heavier than it should) and therefore lets too much gas in the bowl. The float height is critical for proper running.
Remove the bowl. Look to see if nothing sticking like the inlet needle or float itself. Turn carb upside down to the float should be parallel to carb body.(different manufacturers specify different heights but adjusting the float parallel to carb body will run good.) Remove pin from float hinge to remove float. Check to see if the float is leaking, even just a small amount of gas in float makes it heavier and therefore lets in too much fuel. It can be difficult to see if it is leaking, shake back and forth to try to find out. If the float inlet needle or float itself is not sticking I suggest you get a new float. Adjust it to be level with carb body by bending the tang that sits on inlet needle. It should be pretty well level just as is.
I suggest you try that and see what happens. But as long as you have carb apart clean it with carb cleaner or paint thinners and blow air in all ports (low pressure air). How old is the gas in the tank? If over one year old use fresh gas. Try that and see what happens. If still problems I am willing to answer any of your questions. I hope this helps a little bit. Regards and good luck.

If it will start when you pour gas then its a fuel problem on some of these they have a screw at the bottom of the carb remove that and see if you have bad fuel. If that does not work then remove the carb and service it may just be a stuck float or something

firstly, the answer re fuel going up the line is YES!

It sounds like a lack of compression. Take out sparkplug and place finger over cavity whilst pulling starter cord. The pressure should be strong enough to push your finger off the hole. If not, then the rings are shot or there is a hole in the top of the piston.

This will cause poor run in the fuel line to the carburetor. so the carbi is possibly empty or not full enough. Check the float level or that the float, actually floats. It sounds that that float is OK as its not flooding, but take a look anyway it may be jammed shut.
Lastly.. check the spark lead where it goes inside the body as this screws onto a screw to make contact with the inside of the leed. Get a new leed as these carbon based leeds fail after a short time anyway.

Presumne you checked it was actually sparking well?
These are the things that commonly affect chain saws and brush cutters

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Check the oil hole filler and see if the oil has fuel in it. This is a good indication of poor rings and holes in psiton

carburator float is stuck in the open position allowing fuel to continiously run / drain out the fuel tank into the carb and then overflow into the venturi of the carb into the engine and out the air filter. Bottom line the carb needs to be disassembled cleaned and rebuilt

if you are getting no fuel to the plug you either have a stuck float, plugged fuel line or filter. does the gas reach the carb bowl? does the mower have a fuel pump? if so the diaphram might be bad.