Just got a super XL automatic. Looks pretty good now that it's cleaned up. It wants to start, but only fires a little. Never had one this old. It's got a thumb pump for killing the bar. Lol. Lol its like trying to drop crank a concrete block. Talk to me friends I'm gonna need your help.
I usually do the following.
Pull the plug and spray some lubricant in the cylinder turning it over a few times to make sure the flywheel/piston turn freely. WD-40 is fine. Pull the cover on the muffler and visually inspect the piston and cylinder while turning it over. While at it, check for spark. Turn off the ignition and crank it hard several times with the carb choked. If the pump is soft enough and the carb isn't varnished up, it may be enough to get the fuel moving. See if air/fuel mix is being ejected at the spark plug hole. If it sat with fuel in the tank, the factory line is likely gone. If you've no fuel line you can try dropping a small splash of fuel down the carb or in the spark plug hole.
If you've got spark and fuel is moving through the carb it may start. Try 1 1/4 on both L and H. Pretty easy saws to pull the carb from and re-kit. Given the length of time it has sat, new filter, fuel line and carb kit are a given. If the diaphragms in the carb are a bit stiff, you can soften them up by soaking/rubbing in a mixture. I've used methyl hydrate and Seafoam/PB blaster at a ratio of 1:5 for a couple of hours at a time. A short term solution at best. But, it does really soften them up in a hurry.
If it pops like you are suggesting, you may need to repeatedly choke/pop/re-choke +full throttle/pop...etc to find out if it can pull enough fuel to run on its own. Do this with the saw on the ground.