Ryan, I think I know what your problem is. On the larger riding mower engines, there is a compression release built into the engine. Basically it is there to hold the exhaust valve open when the engine is not running. Sometimes this device fails and the valve is left closed. The starter is not strong enough to overcome the compression caused by the closed valve. You may hear a partial turn of the engine and then it won't turn over. So...what to do? Remove the air cleaner so you have full access to the air intake to the carburetor. Put on a leather glove and put it tight over the air intake on the carburetor and keep it there while someone else cranks the engine using the starter normally. The engine should turn over easily and will probably start. BE CAREFUL IN CASE IT BACKFIRES THROUGH THE CARBURETOR. It could burn you.
What you are doing is, you are not allowing any air into the cylinder so there is none to compress! Therefore it will turn over right through the compression cycle without releasing the valve. Once you get it to turn over properly, let it take in some air and fuel. You should be able to get it to run.