follow the leads to the electric clutch attached under the main engine pully the connecter might just have a bunch of old grasss stuck in there.

My dad's old lawn tractor was like that. I would have to put the charger on it to get it started and then it was fine to mow the lawn. The next time out, same thing. I use a push mower and did both my front and back lawn yesterday while tanning. It's good exercise and it starts up with 1 pull! I have a lawn tractor battery in my jet boat and it's been holding up good for several years. At the end of the season I top off the charge and put it in the basement. Most people leave the battery in the lawn tractor and sitting in the garage or shed where it's cold as hell will drain it over time.