If by "not engaging" you mean the fly wheel turns but does not turn the motor, the trip dogs on the fly wheel are either jammed or broken. Normally when you pull the starter cord on a lawn mower or ther small engine, two or four metal flanges, sometimes called trip dogs, extend from the center axle asembly of the fly wheel to engage the motor and turn it. If the cord is pulling freely and retracting as it should, but just not turning the motor, then your problem is almost certainly with the dogs. Remove the fly wheel assembly and examine the dogs. Try turing the wheel in the starting direction to see if they extend. If they are broken or corroded, it is probably best to replace the entire fly wheel assembly. If you do want to replace the dogs (assuming the axle assembly can be opened, usually it is sealed), take care not to damage the recoil spring, which is also inside the axle assembly.
John, September 2004