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usually when assessing an unknown engine that does not start I resort to an orange in line spark tester ( so I can see it in the daylight ) and a can of carb cleaner ( used as starting fluid )
With the tester installed a SHORT shot down the spark plug hole and crank the engne.
If it fires a few times then I can be sure the plug is working and the ignition timing is reasonable .
Then it is a quick shot down the carb mouth and crank again
Engine fires a few times burning off the fuel then I know that the valves are working.
If I can keep the engine running for a minute or so by shooting a small amount of carb cleaner down the carb throat then I know the valve timing is OK and the problem is in the carburettor .
The whole time I watch the spark tester to check the orange flashes are consistant and stable .
Now if it starts quickly and runs all by itself then the problem is with the priming / choke system .
For nice pictorial instructions on cleaning the carb go to
Outdoor Power Equipment carb page