Small Engines (Lawn Mowers, etc.): No start, safety switches, screw terminal

Question
I have just replaced the engine in my LT1018 (Cub Cadet) with another Briggs and Straton model 31g777-0559.  Everything is attached correctly but when I turn key, the engine turns but is getting no spark.  I have tracked back to the yellow wire coming in that connects to black spark wire to engine (meet at harness).  I have checked the black wire for continuity and it is good.  Looking at the schematics, it appears the yellow wire goes back to safety switches.  I am only aware of four safety switches.  The seat, the reverse with blade engaged, the PTO start kill and the clutch swith.  The seat and the reverse switch should not affect the spark.  The PTO is not engaged.  The clutch switch appears to be working as the engine turns fine.  (It won't turn with the clutch not depressed.)  I am now at a loss.  Have verified that gas is good and getting to carb.  Could you tell me where to look next or did I just get a bad coil on the new engine?  I keep thinking the coil is not the issue as there is no power coming through the yellow wire on harness that connects to the fire wire.  I have to be missing something simple.

Answer
No power should go to the engine coil.  POWER is bad on the igntion coil!!!

There should be one spade or screw terminal on the engine for the mower shut-off wire to connect to.  Dis-connect the mower harness from the engine shut-off terminal and check for spark.  If you have spark the coil is fine.  

If there is no spark, then remove the top engine shroud to access the ignition coil.  Dis-connect the small wire connected to the coil.  Check for spark.  If you have spark the coil is good.

Let me know what you find.
Eric