That is one of the things about 2 cycles. They might as simple looking as can be but everything got be working together to be right. Often times here it is multiple problems mainly due to lack of maintenance or the fact they have been sitting for years without use. Most of the handheld usually comes with when they won't start then I find multitude of problems.
With four cycles it not that way. A lot easier to pin point problems but they can be a pain in the rear at times.
So glad that I trained myself on 2 cycle by getting a whole load broken ones from another shop with lots of time and reading I manage to fix over half of them. But boy taking all day to fix one was not profitable but i now got it with experience and troubleshooting skills down to under an hour on most of them. Some are just not fixable any more due OEM changes to short blocks vs a PNC kit as it cost as much as a new unit to repair them.