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If there's too much play you probably need to replace the gears. They seem to be made of cheap material to fail.

I'ld avoid pounding them off or you'll most likely break off the retaining rings inside the transaxle.

I did that recently and they don't make those retaining rings anymore.

If you're sure the battery is good and the connections are tight, it could be a bad starter or solenoid.

Might try looking under the foot rests, I have a older craftsman that has a belt diagram under the left rest.

I recently restored the transaxle and body on this old junker but one part came loose somewhere near the deck while I was removing the rearend.

I didn't get the chance to see where the spring was...