Small Engine Troubleshooting Problems? Ask a Mechanic Now.
Looks to be Briggs engine. If you follow the battery posiitive cable to the starter solenoid, and jump across the two cable terminal with old screwdriver, will the engine spin?
Have you checked the seat switch and the harness to it? It is the most likley to cause no starter action. It also has a brake/clutch switch, and a pto switch. I assume the pto is off?
If the starter does not spin engine when jumping the solenoid, on the first test, the battery or the cables are problem.