First, ensure the battery is GOOD.
The battery on these models is only just big enough to get the job done. If they are not removed from the mower and conditioned regularly, their life is 3 years at best - less if left on the mower for the winter months.
If the engine is a Tecumseh, the starter is a car-type, bolted to the side of the engine. These give little trouble, and if they work at all, any problems are likely to be down to poor connections.
If the engine is a Briggs & Stratton, the starter is a geared type buried under the cowling. The grease can dry out in the reduction gearing, causing them to turn too slowly to start the engine. If this is the case, it will have to be removed and stripped/greased. They can also disintegrate inside - starting with the permanent magnets becoming detached from the housing. If this occurs, a replacement shell with bonded magnets is available at about £30.
phil_saunders(a)bigfoot.com
Phil Saunders, April 2009