Some of those carbs are cheap($25) to buy new. A diaphram kit is about $12 which is a good idea to install if you are opening it up. The diaphram(fuel pump, round aluminum on it) should be dry on one side and wet on the other. If it is wet on both sides, it is no good.
I can't tell from that pic but I have cut notches in the adjustment screws and tried adjusting it. I can't tell if those are permanent or adjustable.
If it is more than 4 years old, I would cut losses and buy a new machine. The $100 one's from Walmart, Home Depot, Sears and Lowes are disposable. If you get 3 troublefree years out of them, you have done well.