Basically it's barely ever the wiring
it's either compression, spark or fuelmix. (no engine needs more than those three things to run)
since it's a small two stroke I assume it's a piston port ..
in which case as long as the piston rings are still intact (grinding noise if not) and the head gasket is as well compression should be okay'ish at least.
spark.. even if you test the plug (holding it to the engine and watching it spark)
doesn't mean that the plug will fire INSIDE the engine, or is strong enough to ignite the fuel properly.
So get a new plug and test it again.
Oh no wait.. if it's got a CDI module (say it's a scooter engine) it might indeed be the wiring,
but frankly.. as long as the kill switch isn't engaged, and it pops (not just turns) while the starter button is pressed.. it's NOT an electric problem at all

but still if the CDI isn't working or not working properly it's a "no spark" situation again
Have you cleaned the carb? yourself? properly? including poking all jets and breather holes? twice?
No, well.. try again... we've seen carbs that started to work properly after a third and fourth thorough cleaning process only.
(have you reset the adjusters after cleaning?? try that first! full in, then two and a half turns out should at least stay running, however lousy)
But we need pics.. better a video of you trying to start it (to hear it)
maybe we can even tell make and model of the engine...
'sid