I've had this problem with several leaf blowers and a snowblower that were all donated to me.
The problem is in the carburettor. If you are careful and posess a modicum of intelligence which I'm sure you do, it is not hard to strip the carb down and clean it.
You need a couple of basic tools, some carb cleaner and a rebuild kit - Home Depot maybe - if not a small motor repair or online store - $10-$15. One thing to look for - there is usually a small seal between the main jet and the float bowl. This has been known to swell and block the fuel flow. Make sure you replace that.
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Thanks very much and good luck.