The gas is "pumped" from the tank by impulse pressure changes of the crankcase being applied to the crab pump diaphragm. The impulse line connects to the carb end cover plate. The fuel hose connects to the side elbow.
Generally, if the saw has been stored for a while the carb is gummed up. Pull the carb, clean out the gunk with White spirit (Coleman stove fluid) and put a new kit in it. Obviously check the integrity of the impulse and fuel lines, and put in a new fuel filter. It might be that you have an air leak from a crank seal, but most likely you just need to fix the carb.
An easy was to check the fuel flow to the carb is just connect another fuel source (like a weedeater tank) to the side elbow, and gravity feed it. If the saw runs fine, the problem is impulse; if not, fix the carb.
Make sure your H+L screws are adjusted to "standard" settings before getting too deep into the problem. I'd start with 1 1/8 turns out from seated.