I've rebuilt a bunch of 024/026 saws and they're super easy to work on as long as you have a T27 long driver and 8mm spin tight driver.
If it fires and runs with fuel down the carburetor throat then dies out, the compression is still marginal to good, but something in the fuel delivery system is the issue.
This includes fuel lines, crankshaft seals, carburetor cylinder boot, plugged fuel filters, leaking fuel lines, an ethanol damaged metering diaphragm, or one or both debris clogged jets.
If you have good spark and you can't get the saw to run briefly with fuel down the carburetor throat chances are the compression is the issue.
If the fuel down the throat starts the engine and it continues to run and revs then stumbles open the High jet ( one closest to the airfilter) a 1/4 turn and repeat.
If it still doesn't run, run the adjustments all the way in then back out to the original position and try starting it again.
If it still doesn't run back out the High jet another 1/4 turn and try to start it again.
If it doesn't run properly pull the carburetor and check the fuel filter screen and metering diaphragm.
If those look good, swap in a different carburetor.
If that doesn't work check the fuel line, fuel filter, impulse line, and carburetor cylinder boot for defects.
The last easy thing do check the torque on the mounting bolts and tighten as needed, if those are normal pull the cylinder and check the piston and cylinder bore for scoring, and also check is the cylinder gasket.
If all these look good, time do a vacuum test or just replace the crank shaft seals.