A bad battery will fool a multimeter. I've had it happen before. Voltage will show good even with very poor amperage. Voltage is potential, Amperage is power to do the work.
I suggest you go back to your training that covered voltage drop testing. If you are not familiar with this form of testing, just ask.
Maybe some diagrams would help:
Parts lookup and repair parts diagrams for outdoor equipment like Toro mowers, Cub Cadet tractors, Husqvarna chainsaws, Echo trimmers, Briggs engines, etc.
www.partstree.com