Thanks for the ideas with the carburetor. It probably is something like that. But another thing I noticed is that the piston in the intake is down, and doesn't appear to work. The owner's manuel suggests this as one of the problems for not starting in the owner's manuel. But I decided the best thing would be to get a brand new carburetor. I found one on ebay, and I decided to buy it and see if it would work. It is only like $60 including shipping.
And for the engine, it is a used one, but it has almost no miles on it, looks great and I am pretty sure it has good compression. I was thinking it was possibly even a valve problem, like maybe they were not adjusted correctly, but the way it starts plugged and with carb cleaner spray, it has to be a carb problem.
Another thing I noticed is that the breather tube going from the back of the air filter to the transmission was not in quite right, and I can not get it in. I do not think that this has to do with the carb problem, but I would like to now what this is really for and if it is ok to run with it out. I appreciate the help so far.