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As far as the weed whackers, I too have 3 and none of them run properly! Two of them only run on half choke, and thus only give you about half power, and the other one, despite being super clean and only 2 years old, will not start at all! What the hell, ya know?!
As a guy that used to run a small engine shop I can tell you what probably happened. Everyone knows to check for compression but two-strokes need a good lower end seal to draw the fuel/air charge into the engine. More often than you would think the crank seals go bad while sitting, might be ethanol in the gas, might just be crappy seals but regardless the result is you can do whatever you like to the carb or spark plug but no amount of pulling will get them to start.
Since I had to quickly diagnose these things I developed a protocol.
1. pull the starter rope to make sure there's compression and the cylinder isn't stuck.
2. drain the old fuel
3. check for spark, install new plug since I bought them by the gross.
4. remove air cleaner and shoot a little carb cleaner in.
5. give it another pull and see if it fires.
6. if it fires put fresh mix gas in and see if it will run
7. if it only runs on choke clean the carb and maybe put a kit in
8. if none of the above works scrap it out unless it's a high end unit that is worth fixing
The problem with these things is the only way to check crank seals is pulling it apart and fitting blanks to seal off intake and exhaust ports then pressure check. Unless it's a high end unit and you already have the sealing blanks this is about two hours more labor than a replacement tool will cost. if you can get it running you can shoot a little carb cleaner at the ends of the crank to see if it makes it run better but that's really hit or miss. Honestly, if you get to step 6 and you're not trimming the chance of it ever working is pretty small. Sometimes replacing the primer bulb or fuel lines will do the trick but you can see that problem.
Reality is I've already spent more time typing this up than it takes me to troubleshoot a cheap weedwhipper
My honest suggestion is when one of these things doesn't start you really have two options. If you have a huge yard and need to trim every week invest in a good straight shaft trimmer and only use ethanol free gas + drain it whenever you won't need it for a month. Or, if you're smart like me get an electric one. The corded units are super cheap and the battery powered ones are good enough now to replace gas powered for most homeowners. Bonus points for getting the one that takes the same batteries as your drills and impacts.
Cheers,
John