I think it is time to get this sorted - the compression and piston condition must be good to start with - if you haven't, pull the muffler off and look at the piston - a pic would be good. When you pull the saw over slowly, as the piston goes through its compression stroke, does it feel nice and spongey or is it just too easy and slack? If you lift the saw off the deck with the recoil handle, does it just tumble downwards or stick for 1-3 seconds on each compression stroke (TDC)?
If that bit is OK, it is likely that you have enough fuel for idle (low speed circuit) but not enough for high speed running (High speed circuit).
If you haven't...change the fuel filter, it DOES make a difference.
Then try the low screw on 1.5 turns and the H screw on 2 turns out. The saw should at least pickup on these settings.
If it doesn't, try H screw 3 then 4 then 5 turns out - note any differences and come back to us.
If still no joy, take the H screw out and give it a good blast of carb cleaner and reassemble L 1.5 turns and H 2 turns and try again.
If still no joy, there is a slight possibility the check valve is stuck shut - when blasting the carb cleaner down the H screw - look at the end of the check valve in the carb bore and make sure the cleaner is coming through the nozzle in to the bore of the carb (Middle bore leading in to the engine).
Worth checking the fuel line for splits - plug one end and blow down the other end - I use a Mityvac pump for this but assume you haven't got one!
If that doesn't do it, it is a real oddity!!!!
BMP - spot on on accelerator pump issues, air gets past and is then injected in to the check valve giving all sorts of idle issues BUT....high speed generally works OK and it isn't a sudden issue. A stuck pump (it happens) gives a very flat pickup but the engine will still rev out after a bit of feathering.