Is your plug wet ?

Yes

Have you checked compression ?

Compression is good. If I lay it on it's side for several hours and then try it, it will make a few popping noise and then goes back to no attempt to start. I pulled the exhaust off and tried to start and it attempted to start several times but it was just for a half a second or so. Even though the saw has been rarely used I wanted to be sure it was breathing right.

Your chain can be turned by hand right and not binding up causing the clutch drag then engine down when you try to start it????

IMO Your going to have try to clear the comb chamber beings it's flooding. Several reasons it maybe flooding. operator causing the flooding. carb. needle/seat leaking, weak spring not cutting the fuel off. carb. dirty (probably most likely causing needle to raise off the seat alowing gas to flow (not on new carb.)(not likely beings you replace the carb providing you installed it correctly?).

To clear the saw of flooded condition you will remove the spark plug spray it with carb. cleaner, spray carb. cleaner down the spark plug hole (3 or 4 second blast) pull the rope ( this will remove all the oily gas and reprime the comb. chamber). Depending on how much gas has filled the crank case you may have to pull the rope several time repeating the blast of carb. cleaner couple of time.

Now you got the saw clear of all the mixed gas (oil in gas has to be right precentage or it floods and spark plug will not lite off raw gas sloching around in the comb. chamber.) install the plug and and attempt to start. it should fire right off the carb. cleaner (rev up then die) if it dies prime it again with 2 second blast of carb. cleaner down the carb. venturi. it should fire and rev up after couple of pulls on the rope. Hopefully it will take off and run. With new carb. install properly it should take off and run after the flooded condition is removed providing the H and L setting are close to let it run???