Questioni sent you a email about my tractor. the serial #is 917.270913
AnswerMy bad...I think my eyes are going bad...found your question just like you said.
Here is you engine model and type number:42E707 2631
You have a classic "L" engine. I checked the wiring diagram on Sears.com and saw three safety switches; deck, clutch and seat. Here is one of the switches: http://www.shakyparts.com/9665_safety_switch.html
You can remove the top metal engine shroud and dis-connect the small wire connected to the coil. Remove the spark plugs and use and inline spark tester to check for spark. If you have spark with the small wire dis-connected from the coil, then the coil is fine and you know you hava a safety/interlock or wiring problem.
Did trace each wire from the key switch to the safety switches to ensure the connectors are connected? I have seen a lot of connectors come loose causing the mower not to start.
Let me know.
Eric