Update:
I got the mower going again. I had to clean the carb twice. It still didn't want to start. Grrrr. I had spark and fuel. I then got the bright idea (as a last resort before giving up) of trying another spark plug.....and what do you know. It started first pull with the new plug! The old one must have become defective, even though it gave a spark.
Here is some advice for all those guys who don't try basic things first: Just do it! Check all the simple things first. Change out your plug even though it looks OK. Check that you have fuel. Check that the petcock is open. Check that there is no air getting through the side of the carb. These checks could save you the hassle of doing things that you don't have to do.
The worst thing about getting it started was that I then had to cut the grass.
