I have the same mower with a slightly larger engine.
Year before last it started running worse and worse, to the point I had to keep the choke fully on for it to even run.
Finally it got to the point it wouldn't run at all. I dug into the carburetor and there's a jet that's behind an access plug on the side of the carb. I used some small wire to clean it out and it's been running perfectly ever since.
That said, mowers are not hard to work on but you have to have patience to go beyond spraying things in the carb to see if it'll fix it.
If it's got gas coming to the carb, and it runs on starting fluid, the problem is IN the carb, nowhere else. Probably clogged.