Hi, Doc! Depending on the age of the saw, it might be a decent one. In any case, it was probably a good learning experience and possibly fun...there's value there, for sure.
A few questions need to be asked...
How long has the saw been sitting and was it stored with fuel in it?
How is the carb set now and have you attempted to adjust it?
In general, a good starting point for carb adjustments is one turn out on each of the L and H screws from their seated position (seat them lightly, they're sensitive), provided they don't have limiter caps.
Your first goal is to get the saw started, then get it to run with the choke OFF. Once the saws "pops" with the choke ON, the choke has done its job, turn it off, or you'll just flood the saw. Now try to start the saw with the choke off. If you can get the saw to run a little at the settings above, you're probably in business. The L screw position will determine whether the saw starts, so that's the one you'll mess with (in small increments) to get it to idle.
Try that stuff, ignoring the H screw for now. ONCE you get the saw started and idling, it will be time to figure out where the H screw will be for your saw.
All this assumes that your carb is not gummed up! If the the saw has been stored for a long time with mix in the carb, it will probably need a rebuild. It is ALWAYS a good policy to check your fuel line and filters also. In fact, since you've done the piston, I would just go ahead and do a carb kit on general principal. It's cheap and easy compared to what you just went through to do the piston.
What source did you use to fiind the piston and how much did they charge?...I need one cheap!
Oh, let us know the results... what happens when you try to do the above procedures can be used for diagnostic purposes.