First thing is to replace the gas/oil mix. Small engines won’t run well on old gas. I use the 93 octane in my auger. I just went through problems with my auger and have bought Stable for my gas mixture this time to extend it’s life.
It would only “kind of run” on full choke after using some either to get it started. So, I took apart the carb and removed the needle valve (which looked clean) and ran a small bread wrapper tie wire through the openings. There was no way to get a wire through the jet openings, so I sprayed carb cleaner into a small hose and then blew it through to insure they were open.
One of the problems that occur with these small engines is that after a few years, the thin rubber diaphragm will develop a small crack and then will not allow sufficient pressure to activate the needle, so you may need to replace this diaphragm.
earlier this year, when getting my power washer working, I had found the rubber tip on the needle to soften and degrade to the consistency of bubble gum and would not pass gas. So, look at the quality of the rubber point of the needle. If in question, pick up a kit and replace it and the diaphragm.
When you reassemble the carb, make sure you get the gaskets on both sides of the spacer against the block. I accidentally forgot the gasket between this spacer and the carb in my reassembly and my auger ran pretty poor, which had me puzzled why it would not run after a good cleaning with everything looking good.
After reassembly, my auger took right off and runs smooth. I still question if the problem wasn’t due simply to my usage of summer gas from my weed whip….