Ok, well that is a whole 'nother can o' beans.
I am going to start with the simple and cheap stuff first.
We can go much deeper if necesary.
There are only 4 things needed for a spark fired 2 stroke engine to run.
1. Air mixed with fuel at the correct ratio (carburetor).
2. Compression to squish the air and fuel for a good bang.
3. Ignition both strong and occurring at the correct point of crankshaft rotation to start the bang.
4. Get it turning over.
Air, there is plenty of it.
Fuel, old fuel is no good. There is not enough bang in it for the engine to run right.
Modern gasoline goes bad in 1 month, even sooner if it is an ethanol blend.
How old is the gas you used to mix with oil to make the fuel?
Assuming that the carburetor is ok...
Compression, you seem to have plenty of it!
Spark, The spark plug can tell us alot before we even check it for function.
After trying to start the engine for a while, remove the spark plug.
Is is wet? That would indicate that either the spark is not occurring at all or the carburetor is mixing too much fuel with the air.
It also could be a bad spark plug. A spark plug can spark a really nice, fat, blue-white spark when just resting on the cylinder head, but...
The conditions inside the combustion chamber are alot different than sitting on a cylinder head fin and a spark plug can fail under the strains of compression.
Speaking of that fat, blue-white spark, if it is instead a thin spark and yellowish in color, that is a weak spark. That will not have enough umph to operate the spark plug when under the strains of compression.
Check for loose electrical connections.
Is it dry? That would indicate that the carburetor is not mixing enough fuel with the air.
It could be a failure to get fuel to the carburetor from the fuel tank, a clogged fuel jet, or one that the factory forgot to install, or there is a very large intake leak. Using the choke should be able to overcome a small intake leak and at least get the engine started, but not running right. The choke sometimes can be of no help at all with a large enough intake leak.