There is not much to these things:
A) Watch for deteriorated plastic fuel line from tank to carb...plastic falls apart and won't hold siphon.
B) Solid state ignition either works or doesn't.
Bb) Go to northern.com and buy a $7 ignition module and replace the existing one, (Sears will charge you more than the cost of machine replacement for theirs)
C) Re-route the spark plug wire to be sure it didn't break the wire inside the wire...use wire and not carbon interior wire.
D) Shoot spark plug hole with starting fluid to be sure the spark isn't okay...maybe you didn't check it so well, or you are just inept??
E) Throw it away and buy a 4 stroke unit that doesn't have all these issues and is NOT a throw away each year...mine has brush head and works very well going on 5 years. But don't try and weedwack under water with it....use your snowmobile for that job!