I do not have a diagram for that machine here, but I do know that the cause is one switch is stuck closed. Or a wire is shorted giving the same effect. A broken wire giving can also be a cause, too.
The logical reasoning is simple: All safety switches follow a simple rule.... Normally open or normally closed. You must look at the wiring diagram and it will (or should) have each switch marked NO or NC. This depends on the condition, but will be marked with no person on the seat.
So, with a NC (Normally Closed with no person on the seat), then it follows that that switch should be making contact. If NO Normally Open (with no person on the seat) then again it follows that this switch will be open circuit in the no person on the seat condition.
Okay: So we now know where we start from. Set all manual (driver operated) switches to the OFF position. Check the switches are OPEN with a multimeter set to continuity (tone on short) if fitted, or low ohms range. All readings will or should show OPEN. If not, then that switch is faulty.
Now, go round each safety switch in turn and, from the electrical drawing, determine what state that switch should be in with driver 'NOT SEATED'. Some switches will have to be open for the engine to start, and some switched will have to be closed for the engine to start. These have been eliminated, but for the average Yahoo Answers reader that is the norm. Any other state and the engine will not start as was stated.
We now come to the seat switch. This switch MUST be closed for current to flow to the PTO switch.
You must remove all wires that have by-passed switches and rest these to factory setting or you will not eliminate the bad switch or contact.
All ground wires must first be shown to be in good condition, that is: not frayed against frame or broken either externally or internally in the wiring loom, so buzz these out first for the purpose of elimination. A broken wire can be easily fixed with bullet connectors. Relays (if fitted) must first be shown to be functioning and that contacts are clean and not burned or burned closed when they should be open or vise-versa. Any power diode should be checked in the normal way for functionality.
mmalky: 50 years diagnosing and repairing large and small lawnmower engines.