If a starter is able to crank the engine but it won't start you usually have either an electrical or fuel problem. It's also remotely possibly that it's compression.
If an engine has proper fuel,...
the inertia provided to flywheel (by Kick or Servo Motor) provides motion to the crank which in advance compresses the fuel-air mixture in cylinder, and thus ignited by spark plug
Could be the O2 sensor, which is attached to the exhaust. Has your engine management light been on? If yes chances are it is this sensor. Careful when buying a new one as there are many different...