Several times I have seen a saw get "hard to start" (or impossible) due to increased compression. It is almost always fuel leaking into the case, and most often the fuel lever on the carb. Sometimes the plunger (with seal) needs to be replaced, sometimes it is just the fuel lever is set wrong (this usually only occurs if it is a new carb or if the saw has been worked on, or the carb rebuilt).
Another annoying thing if a saw won't start is when the flywheel key has sheared. If you pour a bit of fuel in the back of the carb and the saw fires OK, this is not it!