Okay, I got home and checked the orientation of the coil. It was upside down. I turned it over and gave the string the ol' heave ho and...nothing. It gave a little sputter like before as if it was trying to start, but just once. More pulling got no sound at all except cursing from me. It sounds like it's starved for fuel. By the way, the horn sound occurs when the fly wheel feels like it's rubbing on something. I just don't see anything. The shiny metal I saw around the base of the flywheel is from the brake. I don't care about the sound so much as the fact that the fly wheel won't turn freely in one spot.
@bertsmobile1: The first coil I got was a compatible that wouldn't even fit on my mower. I will return that one. The second one off of Amazon is also compatible, but at least it fits the bolt holes on the mower. I kind of regret that I went for the cheaper one now, but I'll see if I can see a spark on it and if not, return that too. Live and learn.
This weekend I'll try cleaning the carb again. Maybe I missed a hole. Thanks for the advice, guys. I need all I can get.
I wrote this a while back and to save a lot of typing copied it here.
Read it an take what you need form it.
Lawn mower diagnosis 101.
Get an in line spark tester or better still a colortune and fit it
Get a can of starter fluid.
Remove air filter, give the mower a shot and try to start it.
If it starts but will only continue running is you keep giving it short shots of starter fluid the you have a fuel problem
If the colortune / spark tester does not flash or stops flashing before the engine starts to die, you have an ignition problem.
get a temporary fuel tank
Hook it directly to your carb and hold it as high as you can above the mower to give you the best head pressure.
Runs OK then you have a fuel line problem
No difference then you have a carb / manifold / valve problem.
Hook up the original fuel line again , start the engine & keep it running with short shots of starter fluid.
With a TRIGGER bottle of water/ Wd40 etc liberally spray all around the intake manifold.
Engine speed changes = air leak