Disappointing weekend:

Have a 18.5hp, 46" Rider from Murray. Model 46570x8A
Ran it till it was completely out of gas.
Filled it back up, and tried to start it. Repeatedly. Engine turns
over fine, but doesn't catch.
Tried till the battery needed a jump start. (Took breaks to keep from
hurting the starter.)
2 Days later and can still not get it started.

Debug steps tried so far:
1) Checked under air filter, saw gas squirting into the carb. Also
noticed gas smell from exhaust, while I was trying to start engine.
So, seems to be getting gas. Engine turns over fine, just doesn't
catch.
2) Pulled a spark plug, and rested it on the engine block. Did not
see a spark.
3) Replaced both spark plugs. Still do not get a spark.
4) Confirmed that yellow grounding wire that connects to the Armature
is *not* connected to ground, as long as I either have the brake pedal
down, or the seat switch depressed.
5) Ohm'd out the diode in the red wire that runs from the ignition
switch to the Stator. Looked good.
6) Checked the fuse. Ok.
7) Replaced Ignition Switch. Still doesn't get spark.
8) ... help?!! There's not much left.

I'm looking at the "Parts List" book that came with the mower. Has an
Electrical System diagram, and I have to admit, I'm having trouble
seeing the current flow path that ultimately supplies battery power to
the spark plugs. Of course, I'm not really sure of what a Stator
does, so that's probably the problem. Seems like the Stator and the
Armature are the only things left.

What (how) do I check next???

Thanks!
-Oliver
Raleigh, NC