Hi! Welcome to the site! You need to status the saw's systems. A few basic questions need to be answered:
1. Does the saw have compression? Hold the saw up by the pull rope.....does the saw zip to the ground or does it go down fairly slowly in a series of slow bumps? Its a pretty rough estimation, but this will give you some idea of how healthy compression is.
2. Pop off the muffler and take a peek at the piston and rings. Move the piston using the pull rope to get a look at the back of the cylinder. Do things look pretty clean... or are they scored up?
3. Is there spark? Pull the plug, and with the boot attached, ground the plug against the case and pull the rope. Is there spark? These are old points systems but solid state ignitionare available for cheap.
4. Is the saw getting fuel? Inspect the fuel line for breaks, cracks, dryness, and pliability. When you squeeze it does it spring back to shape quickly or does it look like it might collapse under vacuum? Check your fuel filter (on the end of the fuel line inside the fuel tank.) I uninstall mine and blow through it (mmm, tasty!) to see if it offers resistance. Check to make sure that the carburetor and mounting block are snugged up.
With the plug, plug boot and muffler reinstalled and the air filter and cover uninstalled, add a half teaspoon of fuel to the carb throat. While you're doing it, make sure the saw is tipped down (bar down,rear handle up) and the throttle is depressed so that the fuel will spill into the combustion chamber. Once you've done that, try to start the saw. If the saw starts and and runs for a few secs, you've probabaly just found that your no-run condition is fuel system related.
Although there are exceptions, if you have fuel, spark and compression, the saw will most likely start and run. Do these things, then get back to us with results. We can help you more when you give us more to work with.