Okay, so to date:
The saw does not fire, not even pop.
Will flood fuel through the system until it leeches out of the muffler.
We can assume timed correctly and correct flywheel/coil combo (although not confirmed yet by number checks and if it was not messed with before you got it).
Assume it has good spark with plug outside cylinder and earthed (although spark under compression not verified by inline spark tester).
So, that kind of leads to the compression or lack thereof theory.
If it indeed had a severe lack of compression when you got the saw, any improvement is going to feel good- but good is not always great, nor always ideal.
One rough way to disprove it, if you do not have the correct gauge to test it- is to pull the plug, tip about a teaspoon full of mix oil down the plug hole, on top of the piston- swill it around a bit, replace the plug and start the saw. IF all other ducks are in a row- the oil should give a temporary lining to the cylinder wall/rings that will boost compression and allow a saw with weak compression to start.
It will smoke like a mosquito fogger- but it should run.