Hi All,
First of all, thanks to all who made suggestions. I finally was able to get back to this engine to try it out and yes, I do know how to check for spark since I have been doing that for over 50 years at the spark plug. Nowadays, I use one of the spark plug testers like you can get at HF for about $5 which makes it easy to put between the plug wire and the plug. You don't have to hold the spark plug threads tight against a ground, turn engine and look for the spark at the same time.
Anyway, I was reading about the primary and secondary circuits on magnetos which got me to thinking that there must be a sequence to which side of the magnetron senses the magnet first. Bottom line was I took it off and flipped it upside down, turned the starter and had spark! I then tried to start it, and it cranked right up. I shorted out the kill wire with a screwdriver and then attached it. Working fine now. I looked back at the instructions that came with the new B&S magnetron and it never said which side was the top. There is a little sketch, but it doesn't say whether it is top or bottom view. BTW, I had made sure I put the replacement magnetron on with the spark plug wire and kill wire in the same positions as the old one. In fact, I looked back at the old one again, and you could tell by the crud around the screws which way it had been on. However, the original magnetron has been replaced by another part number so I suspect the wiring is different with the new part. That's the only thing I can think of because the engine had run fine for years. I had never taken the cover off before all of this and had never touched the magnetron before.
So after reading all of the stuff on-line about how if the engine turns fast enough, magnet is good, gap is right, kill wire is not connected, you should have spark from the magnetron. The missing info is that the magnetron has to be right side up! So if you put a new one on and don't get spark with everything else okay, you might want to flip it over since it will mount either way, or at least mine will.
Thanks again for everyone's suggestions.