The check valve is in the main discharge nozzle. The symptoms of a malfunctioning check valve are like the saw running out of fuel (because it does).
The valve sometimes get damaged when someone uses compressed air on them. However, it may have something underneath the thin flutter valve that is keeping it from sealing. If you punch it out of the carb, you can try flushing it out with some spray liquid like WD-40, brake cleaner, contact cleaner, etc. Once you have the nozzle out of the carb, check to see that there is still a valve in the nozzle and that it isn't stuck or damaged. If it looks OK, then with the nozzle out you can get access to the little hole that feeds fuel to the check valve. Try spraying the liquid in the hole. - Or, put a replacement nozzle in the carb.