When I have problems starting a small 2-stroke engine after priming and choking it and pulling it over a number of times, I go through a troubleshooting routine:
I pull the plug to see if it is dry or damp with fuel. If damp, I turn the choke off and open the throttle fully while I pull it over with the exhaust pointing down. This will allow excess fuel to be pumped out of the lower end and cylinder and out of the exhaust port. I then place a finger over the plug hole and pull the engine over slowly to check for a strong suction/pressure pulse as the engine turns over. If it is strong, I place my palm over the carb inlet to check for a strong vacuum when I pull the engine over slowly. If the vacuum/pressure tests are poor, it is time to consider disassembling the engine to inspect the piston and ring, and the cylinder condition, and/or the lower end bearing(s) and seals. I have found engines with low compression that had a ring stuck in the ring groove of the piston, although there was no other damage to the piston or cylinder wall.
If the vacuum/pressure tests are ok, I connect the plug to the plug wire, ground the plug body, and check for spark when I pull it over. If ok, I reinstall the plug, if not, I try a new plug to see if it will spark when pulled over. If no spark with either plug, it is time to troubleshoot/repair the ignition system.
If the plug sparks, and it was dry when I first removed it, I spray starting fluid into the carb inlet before trying to pull start it. If the engine fires but cuts off right away, the fuel system is due for troubleshooting/repair.
This procedure will not catch every possible problem, but it doesn't cost anything, and it is relatively quick to perform.