[Harryc]

IMHO, I'd want to try everything before I went here .
http://www.smallenginewarehouse.com/RepowerItems.asp?Brand=John Deere&Model=318

Can you turn over the engine by hand?

 

[Harryc]

Check fuel. Pull the fuel line from the carb and point it into a container. Try to start the engine. Does gas flow consistently into the container while the engine spins? Also, check for cylinder movement. Pull the plug/s and shine a light into the spark plug hole/s while cranking the engine. Do you see movement of each cylinder?

 

[Harryc]

After you start cranking the engine, the gas 'should' start pouring out of the fuel line in a matter of moments.

 

[Harryc]

You don't want to mess with the starter mounting position because the flywheel may not be cheap to replace. It should work bolted up correctly. My advice, get a new starter.