Small Engines (Lawn Mowers, etc.): no spark, safety switches, ariens

Question
I have a Ariens HT 16 (model # 934001) with a 16hp Briggs (model # 402707 type 0140 0).  I bought this used with snowblower attachment on tractor already, around end of October 2011.  Started about 6 or 7 times, and ran fine and to make sure all was good.  Then we got snow around beginning of January 2012.  And went to start and no spark.  So figured bad coil but did disconnect ground to coil just to eliminate all safety switches, and still no spark.  Battery full charge, and check flywheel key, and key is not sheared.  Ordered new coil, put on, gap adjusted with bisness card and feeler gauge at .010.  Turned over, and no spark.  Ok, thought this is bad coil too.  Ordered another coil, put on and again no spark.  These 2 coils are made by Rotary...part # ROT-0 8051.  So ordered Briggs coil...part # BS394891.  Put the Briggs coil on, and guess what, again still no spark.  And with all these coils, I didn't hook up the ground via kill switch.  Now don't know what to think anymore.

Answer
Were the coils marked with "This side up" to make sure they are not installed upside down?

How are you testing for spark?  Are you using an inline spark tool or just the spark plug?  Did you replace the spark plugs?

What is the code number?  Does the engine have points?

Eric