My parents Simplicity 52" did the same thing. I would first take battery to parts store for a load test. If that checks out, start cleaning all electrical connections. Amazing what gets inbetween connectors. I pressure wash their rider a few times a year and use dielectric grease on electrical connections.
With 20 plus years dealing with riding lawnmowers, I would say it's the battery...and would clean all connections in the starting system.
The PTO isssue sounds like a bearing going bad in one of the deck pulleys. When one seizes up, the belt will still keep spinning yet the pulley/guide will be seized or dragging. Make sure your PTO lever fully engages and disengages the drive.
Si Vis Pacem Parabellum
1967 Starlight black PMD Engineering 400 Auto 1968 Alpine Blue 400 4 speed 1968 Verdoro Green 400 HO 4 speed 2013 1LE 2SS/RS Inferno Orange Camaro.
