Might get more responses in the chainsaw forum.
If it fires when you add gas the fuel over pressure in tank is not the problem, but there should be a vent for the tank.
Does the choke work? If the tank filter is clogged that could be the culprit.
When taking the carb apart be sure you don't mix things up and keep arranged in the order removed.
The carb has two diaphragms, one that pumps the gas the other that helps meter the gas. These are under the covers on the top/bottom of the carb. If you are careful you can take the covers off and not rip the gaskets/diaphragms. Check the diaphragms for cracks/tears, hold them up to the light. Make sure the meter side is not full of sawdust under the cover that makes its way in through the covers vent, it won't pump full of crud under the cover. There is also a screen/strainer on pump side be sure that is clean. On the metering side there is a needle/lever/spring assy that sits under the diaphragm. Make sure it is free and and the seat on the needle and carb are smooth/clean.
If all this checks out then the carb may need cleaning and you might as well replace things with a rebuild kit. If you have access to a sonocator they work great on carbs, if not blow out all the passages with some carb cleaner.
Before you do that check the impulse hose that runs from the crankcase, it needs to deliver vacuum to pump the carb. Use the proper hose not a piece of tubing if you need to replace it.
One more thought. As mentioned you need crankcase vacuum to pump the gas. Be sure that the cylinder has a good seal at the base gasket you replaced and check the cylinder bolts are tight.
If you have a good saw shop nearby bring it in for a vacuum/pressure test, the other place air leaks happen are the crank seals. I'd check over the carb and what I've mentioned first before a vacuum test.
